022872-2-TM Determination of the Liquid Water Content of Snow by Freezing Calorimetry Richard T. XAustin U.S. Army Research Office Box 12211 Research Triangle Park, NC 27709 Contract DAAG29-85-K-0220 January, 1990 Radiation Laboratory

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Determination of the Liquid Water Content of Snow by Freezing Calorimetry Richard T. Austin

Determination of the Liquid Water Content of Snow by Freezing Calorimetry Richard T. Austin The snow gravimetric liquid water content is perhaps the most important parameter that influences the radar backscatter from a snowpack. This is due to the large difference in the relative dielectric constants of liquid water (= 10 - j20 at 35 GHz) and ice (= 3.15). Thus even a small amount of liquid water in a snowpack can cause a dramatic change in the backscatter characteristics of the snow. Freezing calorimetry is widely regarded as the most accurate technique for determining the liquid water content of snowl 2, although the procedure is tedious and difficult to perform in the field. It is based on straightforward equations of heat transfer. The procedure is relatively simple: a sample of snow of known mass and temperature is added to a calorimeter containing a known mass of a liquid freezing agent. The temperature of the freezing agent is monitored both before and after the snow sample is added. The mixture is agitated until all liquid water in the snow sample has frozen and the mixture has reached an equilibrium temperature. Since the heat capacities of the freezing agent and water and the latent heat of fusion of water are known, the amount of water initially in the liquid state can be determined. Derivation of Calorimeter Equation There are two cases, depending on whether the snow "temperature" Ts is above or below Tz, the freezing point of water (273.15 K or 0 ~C). I write "temperature" because the idea of snow temperature is somewhat vague. Snow is a mixture of air, liquid water, and ice. In the following formulation, we assume that the snow is isothermic, that is, it has a constant temperature throughout the sample. If this were true, a snow sample at a temperature above Tz would be purely liquid, while a sample below Tz would be completely frozen. Thus our liquid water measurement would be unnecessary, except for the rare case of 0 ~C snow. Clearly, snow is not isothermal, even within small samples. We will refer to a snow temperature Ts and understand that this represents a mean temperature which is measured with a thermometer or probe inserted in the snowpack. 1E. B. Jones, NASA Snowpack Ground-Truth Manual, NASA CR 170584, May 1983. 2W. H. Stiles and F. T. Ulaby, Microwave Remote Sensing of Snowpacks, NASA Contractor Report 3263, June 1980. 1

If the snow temperature Ts is greater than Tz, we have =T Tf Tf Tf Tf Hf = H + mwCw dT + mwCd dT + JdCd dT+ JACA dT + JmcCc dT- Lmw [.a] Ts Tz Tz Ti Ti while for Ts less than Tz, we have Tf Tf Tf Tf Hf= Hi + mwCd dT + mdCd dT + mACA dT + mCCC dT - Lmw [l.b] Tz Ts Ti Ti where Hf = final heat of calorimeter system (cal) Hi = initial heat of calorimeter system (cal) = Hf mw = mass of liquid water in the snow (g) md = mass of solid component of snow (g) ms = mass of snow (including both liquid and solid components) (g) mA = mass of freezing agent (g) me = mass of calorimeter (g) L = latent heat of fusion of water (cal/g) = 79.7 cal/g Cw = heat capacity of liquid water (cal g-1 K-1) Cd = heat capacity of frozen water (cal g-1 K-1) CA = heat capacity of freezing agent (cal. g1. K-1) CC = heat capacity of calorimeter (cal g-1 K-1) Ti = initial temperature of freezing agent (K) Tf = final temperature of freezing agent/snow mixture (K) Tz = freezing point of water (K) = 273.15 K Ts = temperature of snow sample (K) 2

In addition to the initial and final heats of the system, there are six terms in equations [1.a] and [1.b]: (1) the heat lost by liquid water in the snow as it cools to 273.15 K, (2) the heat lost by liquid water at 273.15 K as it freezes, (3) the heat lost by the liquid water (after freezing) as it cools from 273.15 K to the final temperature, (4) the heat lost by the frozen water in the snow (i.e., the ice crystals in the sample) as it cools from its initial temperature to its final temperature, (5) the heat gained by the calorimeter as it warms to the final temperature, and (6) the heat gained by the freezing agent as it warms to the final temperature. Note that term (1) vanishes if Ts < Tz (Eq. [l.b]). In the above equations, we have assumed that the liquid and solid components of the snow mixture fit one of the following descriptions: a. the liquid component has temperature Ts (> Tz) and the solid component is at Tz; b. the liquid and solid components are at Ts = Tz; or c. the liquid component is at Tz and the solid component is at Ts (< Tz). In other words, we cannot have Tliquid > 273.15 K and Tsolid < 273.15 K simultaneously. We now solve for each case separately, using some simplifying assumptions. First, we assume that the heat capacities (specific heat) of liquid water, ice, and the freezing agent are linear functions of temperature. These are not bad assumptions over the temperature ranges in which we work. The values for the heat capacity of liquid water3 are shown in the following graph: 3Values obtained from CRC Handbook of Chemistry and Physics, 60th Edition, p. D-74. 3

Specific Heat of Water 1.008 - y = 1.1719 - 6.038e-4x R = 0.99 1.006 1.004 1.002 1.000 272 274 276 278 280 282 284 Temp (K) Values of the heat capacity of ice are shown below4: Specific Heat of Ice 0.51 y = -0.0082 + 0.0019x R = 1.00 0.50 0.49 0.48 z 0.47 0.46 i 0.45 0.44 i I 240 250 260 270 280 Temp (K) The determination of the heat capacity of the freezing agent will be described in a later section. A further simplification is performed by assigning a "calorimeter constant", E, with units of grams of the freezing agent. This allows the calorimeter and freezing agent to be lumped into a single term. Using the above two assumptions results in the following equations: 4Values obtained from CRC Handbook of Chemistry and Physics, 60th Edition, p. D-175. 4

for Ts 2 Tz 0 = mwCwsz(Tz - Ts) + mwCdzfTf- Tz) + (ms - mw)CdzfTf- Tz) + (mA + E)CAif(Tf- Ti) - Lmw [2.a] for Ts < Tz 0 = mwCdzf(Tf- Tz) + (ms - mw)Cdsf(Tf- Ts) + (mA + E)CAif(Tf- Ti) - Lmw [2.b] where we have evaluated the integrals using the midpoint rule for linear functions. Terms of the form Cabc represent the heat capacity of a at the average of temperatures Tb and Tc; for example, Cwsz represents the heat capacity of liquid water at temperature (Ts + Tz)/2. These equations can now be solved for the fraction of liquid water mass: mw (mA + E)CAiKTf - Ti) - msCdzf(T - Tf) (T [3 ms ms[L + Cwsz(TsJ- Tz)] mw (mA + E)CAif(Tf - Ti) - msCdsf(Ts - Tf) (T T [3 ms ms[L - Cdsf(Ts - Tf) + Cdzf(Tz - Tf)]' s These equations vary slightly from the equation used in the NASA Snowpack Ground Truth Manual, in which the additional assumptions are made that Ts is always less than or equal to the freezing point of water and term (3) described above is approximated by the heat lost by the liquid water after freezing as it cools from the snow temperature Ts (rather than from 273.15 K) to the final temperature. Calorimeter Constant The calorimeter constant E must be determined before liquid water content measurements can be made. The procedure for determining the calorimeter constant is similar to the liquid water content measurement; the difference is that the freezing agent and quantity of liquid water are known exactly, resulting in a single unknown in the calorimeter equation, which is the calorimeter constant. The freezing agent used in the 1989 snow experiments was a silicon oil. Since the heat capacity of the oil had not yet been determined, ethanol was used as a freezing agent in the determination of the calorimeter constant. Ethanol (200 proof) was obtained from University Stores. The heat capacity of ethanol is well-known and was obtained from Brown and Ziegler (1979)5, which gives a fourth-degree polynomial for the heat 5G. Nelson Brown, Jr., and Waldemer T. Ziegler, "Temperature Dependence of Excess Thermodynamic Properties of Ethanol + n-Heptane and 2-Propanol + n-Heptane Solutions", Journal of Chemical and Engineering Data, Vol. 24, Number 4, 1979, pp. 319-330. 5

capacity in the temperature range 159 K < T < 306 K. The equation used for determining the calorimeter constant can be derived from Tf T f Tf Hf=Hi + fmceCe(T) dT + mweCe(T) dT + mcCc(T) dT [41 Ti Tw Ti where Hf= final heat of calorimeter system (cal) Hi = initial heat of calorimeter system (cal) = Hf mce = mass of cold ethanol (g) mwe = mass of warm ethanol (g) mC = mass of calorimeter (g) Ce(T) = heat capacity of ethanol (cal. g-1 K-1) CC(T) = heat capacity of calorimeter (cal g-1. K-1) Ti = initial temperature of cold ethanol (K) Tf = final temperature of ethanol (K) Tw = initial temperature of warm ethanol (K) The product mcCc(T) is replaced by EeCe(T), where Ee is the calorimeter constant in grams of ethanol. Solving for Ee: Ee = we Ce(T)T eT dT mce [5] Although Ce(T) is almost linear in the region of integration, the integrations were performed analytically on the fourth-order polynomials. The procedure for obtaining the actual masses and temperatures to use in the above equation is exactly like that used in the snow measurements, except that warm and cold ethanol are used in place of a snow sample and freezing agent. The procedure and data reduction are described fully in the section on snow measurements. The calorimeter used was an Aladdin Stanley insulated bottle with a hole drilled in the lid for the temperature probe. After it became apparent that inversion of the calorimeter was necessary to obtain good mixing of the freezing agent and a uniform inner temperature, silicon sealant was used to seal 6

around the thermal probe. Also, the original circular rubber seal under the lid had to be replaced because it became too stiff when exposed to the cold (= -50 ~C) ethanol and tended to leak. A new seal was cut from a sheet of neoprene rubber; it sealed much better. There is a question as to whether the concept of a "calorimeter constant" is valid at all. In all the calorimetric formulations studied (including the one above), the assumption has been made that mcCc(T) = EACA(T), where EA is the calorimeter constant in grams of the freezing agent (oil, ethanol, etc.). This is not true in general over a temperature range-it implies that the thermal response of the calorimeter is just like EA grams of the freezing agent. Such an approximation may be permissible over a small range of temperature, but is probably not true over large temperature ranges. Consider: when we are solving for the amount of liquid water, we obtain the product mwCw, where Cw is at temperature (Ti + Tf) / 2, and we know that Cw(T) is linear with T. Since Cw(T) is known, we can solve for the corresponding mw, and we should get the same value regardless of temperature. mwCw(T) Cw(T) mw Similarly, we measure the "EC" curve of the calorimeter, where its mass is represented by E, the calorimeter constant. We're probably safe in assuming that EC is linear with T, but we have no guarantee that the EC curve is a constant multiple of the heat capacity curve of the oil or ethanol. For example, if the EC curve is not as steep, we obtain a temperature-dependent value of E: EC(T) Cw(T) E In spite of the above arguments, we have had to use the idea of a calorimeter constant. This was due to my inability to measure the "EC product" as a function of temperature. The fifteen "good" calorimeter calibrations are shown in the figure below-the last seven are solid black. These seven were, in my opinion, the most carefully executed; however, they did not result in a nice linear curve for EC(T): 7

"EC Product" 6200 y = 1694.3425 + 15.0722x R = 0.55 6000 U U 5800- * 5600 3 * n n ^^ B,,E 5400- * Last 7 5200 5000 4800- 11.-,.. i' ~. 230 240 250 260 270 280 290 Tif (K) Part of the scatter here could probably have been reduced through a much larger number of trials, but there was not sufficient time to complete such trials. The known heat capacity of ethanol Ce(T) was divided out of the above data, resulting in the following plot: Calorimeter Constant 65 " 1U 60o Ul* -|-. 55 a E * Last 7 50 45. 230 240 250 260 270 280 290 Tif (K) The last seven points (in black) were averaged to obtain a value of 56.91 g ethanol for the calorimeter constant. The standard deviation of these points was 3.34 g (standard deviation/mean = 0.06). We therefore used this value and hoped that the resulting error was not large compared to other errors in our measurements. According to Tom Haddock, the heat capacity of the calorimeter should not change significantly with temperature. 8

Heat Capacity of Silicon Oil The next task was to determine, as a function of temperature, the heat capacity of the silicon oil which served as the freezing agent in the liquid water content measurements. Silicon oil was recommended by Bruce Jones, author of the NASA Snowpack Ground Truth Manual, for its reusability and safety. Toluene had been used previously as a freezing agent, but its low flash point and toxic fumes made its use undesirable. The oil used was Dow Corning 200 fluid (a dimethylpolysiloxane), 5 centistokes viscosity. The heat capacity of the oil was assumed to be linear, in accordance with Jones (1983). The equation used was that given originally for snow measurements [l.a] with Ts replaced by Tw, modified for the case where the water sample is completely liquid: Tz Tf Tf Tf Hf= Hi + mwCw dT + mwCd dT + moCo dT + mcCc dT- Lmw [6 Tw Tz Ti Ti Having assumed that all heat capacities are linear functions of temperature, we can write 0 = mwCwwz(Tz - Tw) + mwCdzf(Tf- Tz) + moCofi(Tf- Ti) + mcCcfi(Tf- Ti) - Lmw [71 Converting to a calorimeter constant Eo: mcCcfi = EoCofi [8 At a given temperature, EeCe = EoCo. We can therefore solve for Cofi: mw[Cwwz(Tw - Tz) + Cdz(Tz - Tf) + L]-EeCefj(Tf- Ti) [9] Cofi =mo(Tf- Ti) 9

After several trials, a curve of Co values was obtained, as shown below. 1.60 1.55- y = 1.1871 + 1.1998e-3x R^2 = 0.090 1.50 A F Co (1-6) le 1.45 -.... Co(1-6g) o 1.40- Co(GE:adj) l.' A Co (7-12) 0 1.35 a Co(7-12g) 1.30- + Co (1-12g) 1.25 GE: y = 1.2680 + 7.8803e-4x R2 = 1.000 1.20-,., ~., ~, 220 230 240 250 260 270 280 Tif (K) The legend notations are explained as follows: Co (1-6), oil heat capacity measurements 1-6; Co (1-6g), the "good" measurements from measurements 1-6; Co (GE: adj), values given in Jones (1983) for silicon fluid minus a constant (this was plotted to see if our fluid's heat capacity had the same slope); Co (712), oil heat capacity measurements 7-12; Co (7-12g), the "good" measurements from measurements 7-12; Co (1-12g), "good" measurements from the entire set of twelve. A line was fit to the values in the last group, Co (1-12g); its equation is shown at the top of the graph. Next a value was obtained for E0, the calorimeter constant in grams of oil. We chose 233.6 K (by averaging the first nine values of Tif in the oil measurements) as the temperature at which we would solve EeCe = EoCo for Eo. The resulting value of Eo was 80.34 g oil. Necessary Equipment The following is a description of the equipment used in the field for liquid water measurements at the Brighton experiment site during the winter of 1989: 1. - Calorimeter The calorimeter consisted of an Aladdin Stanley Thermos-type wide-mouth insulating bottle (24 ounce size). A small hole was drilled in the lid to allow the insertion of a metallic probe tip containing a 4-wire RTD sensor. The probe fit very snugly into the hole; its diameter was about 8 mm. Silicone sealant was used to seal the lid around the probe. Caution is advised when handling the lid/probe assembly to avoid turning 10

the probe in its hole and breaking the seal. The probe extended about 13 cm into the interior of the calorimeter. 2. HP3468A Digital Multimeter with HPIL option The multimeter was used to monitor the resistance of the RTD probe. The HP-41CX calculator obtained resistance values every 15 seconds and converted the resistance to a temperature. The 4-wire resistance mode was used to increase accuracy. 3. HP-41CX (or compatible) calculator The programmable calculator recorded the calorimeter temperature at 15-second intervals by obtaining the RTD resistance from the multimeter and converting the resistance to a temperature value. Resistance, time, and temperature values were recorded on an HP Thermal Printer for later data reduction. Use of the programmable calculator made the temperature monitoring process almost automatic. (The program used for these measurements is listed at the end of this report.) 4. Connecting cord from RTD to multimeter. 5. HP-IL Module and IL patch cord. 6. HP82143A Thermal Printer and thermal printer paper (black). 7. Outlet Strip and Extension Cord (long enough to reach nearest AC outlet) 8. Electronic Scale The electronic scale is a necessity if measurements are to be made at a reasonable rate. Our electronic scale was enclosed in a plastic carrying box with internal heater to isolate the scale from the wind and keep it warm enough to function (the scale was not designed to operate near 0 ~C). 9. Supply of silicon oil We put silicon oil in 300 ml polyprophylene bottles for ease of use. Each bottle contained enough freezing agent for one measurement run. The bottles were not breakable, were easy to handle, and could be cooled to -40 to -50 ~C. 10. Dry Ice and Cooler The bottles of freezing agent are placed in the cooler with dry ice until cooled to a temperature of approximately -40 to -50 ~C. The dry ice will last about two days in the cooler when purchased in a 50 pound cake. 11. Plastic containers for "wet" oil The oil/ice mixture is dumped into this container after each measurement. Although the large chunks of ice can be strained out by the funnel, the smaller bits of ice must be removed later. The majority of the oil can be recovered. Plastic jugs, such as those used for milk or distilled water, work well. 11

12. Funnels Separate plastic funnels are needed for pouring into the calorimeter and the wet oil container. Large funnels are easier to use when wearing gloves. 13. Paper towels and dish washing tool The calorimeter must be thoroughly cleaned after each measurement. A large supply of paper towels and a dish-washing tool (the type with a sponge attached to a hollow plastic handle) work well for drying or wiping out the inside of the calorimeter. 14. Garbage bags For all those used paper towels. 15. Mercury thermometers for measuring the temperature of the snow sample. These are very fragile, so several extras should be available. The mercury thermometers seemed more reliable than the electronic thermometer. 16. Plastic scoop Used to collect the snow sample. 17. HP Data Cassette Drive (optional) The measurement program is stored on a program cassette. If the calculator loses the program for some reason, having the cassette and cassette drive in the field or nearby will save an unnecessary trip back to the lab. The drive and cassette should probably be kept in a warm place when not being used. Preparation The calorimetric measurements should be conducted in a location which is sheltered from the wind but still at ambient temperature. A table of some sort is needed for the various equipment, and AC power needs to be available within a reasonable distance (closer than the end of your extension cord). It is best to cover the table area with paper towels or plastic before setting up the equipment; this will protect the surface from the oil which will be spilled on it. Plug in the electronic scale first to allow it to warm up. Next, set up the digital multimeter, printer, and calculator. The HP-41CX calculator, thermal printer, and digital multimeter must be connected via the HP interface loop so that the calculator can control the multimeter and process and record the results. A schematic of the set-up is shown below. The procedure for connecting the devices is as follows: a. MAKE SURE THE HP-41CX CALCULATOR IS OFF. This is very important! Connecting or disconnecting the HP-IL module while the calculator is on can result in loss of program memory, which means that you will have to reload the program from tape. 12

b. Insert the HP-IL module into any of the ports on the rear of the HP-41CX. (Keep the port cover handy-you will want to replace it when you are finished.) c. Connect the cables extending from the HP-IL module to the multimeter and the printer-it does not matter which cable goes to which device. d. Use a jumper cable to connect the multimeter and printer directly to each other, thus completing the loop. e. Plug in the AC power cords of the printer, multimeter, and calculator. I? HP3468A r —-~ ~ c l IDigital HP Thermal Printer Multimeter ||4- HP-IL Module O O O ~11 HP-41 CX f. Connect the RTD probe cables to the front of the multimeter (4-wire QW terminals). g. Turn on the printer and multimeter. h. Turn on the HP-41CX. 13

i. Press LQ|, IALPHA|, [, IN, IALPHA. (j[ky indicates a key with the label key; in Alpha mode, the single letters are marked in blue on the keys). This will prevent the calculator from shutting itself off after 10 minutes of inactivity. i. Press Q, ALPHA, W, [, [EM, [, IALPHAi to start the calorimeter program. j. The multimeter will change to 4-wire Q. The "REMOTE" indicator will appear on the multimeter display, indicating that it is being controlled remotely. To make any changes to multimeter settings manually, the LOCAL button must first be pressed. The printer will print a horizontal line. k. The prompt "EMPTY MASS?" will appear on the calculator. The calorimeter should be cooled before the first measurement. Cool the calorimeter by pouring in one bottle of freezing agent and waiting several minutes. The freezing agent can then be poured back into its bottle, re-cooled, and used later. The freezing agent should have a temperature of -40 to -50 ~C (it must be cold enough so that the final temperature after adding the snow sample is still below 0 ~C). Be sure to wipe the inside of the calorimeter before the first measurement. Put the thermometers and snow scoop by the snow pit or sample site. Measurement Procedure When ready to begin a measurement, the calculator should be displaying the "EMPTY MASS?" prompt. If not, press IXEQ, IALPHAI, [, [, IM, [, and ALPHA to start the calorimeter program. The measurement sequence has the following steps: a. Place the empty calorimeter (without the lid) on the electronic scale. Enter the displayed mass (in grams) into the calculator and press R/S. The "MASS W/OIL?" prompt will appear. b. Pour one bottle of freezing agent into the calorimeter. Place the calorimeter (without the lid) on the electronic scale, and enter the mass (in grams) into the calculator and press R/S. The "R/S TO BEGIN" prompt will appear. c. Put the lid on the calorimeter and tighten it securely. Be careful not to twist the probe in the lid. Press R/S|. The "<A> TO ADD" prompt will appear. 14

d. Agitate the calorimeter by inverting it continuously. A complete up-down-up sequence should take approximately two seconds. Be careful not to pull on the RTD wires. Every 15 seconds, the calculator will beep, indicating that the temperature in the calorimeter has been measured via the multimeter and RTD sensor. After the beep, the printer will print the elapsed time in minutes and seconds, the elapsed time in seconds, the freezing agent temperature in degrees Celsius, the freezing agent temperature in kelvins, and the change in temperature from the previous reading. Since the calorimeter is not perfectly insulated, heat will leak in through the walls and lid. The agitation should be continued until the rate of temperature change is roughly constant, indicating that the interior of the calorimeter is at a uniform temperature which is rising steadily due to heat leakage. This usually happens within 5 to 7 minutes. The "equilibrium" temperature rise rate is usually between 0.01 K and 0.1 K in 15 seconds, depending on the absolute temperature. e. When the temperature is rising at a constant (or nearly constant) rate for 90-120 seconds, you are ready to add the snow sample. Press [Ai. The calculator will sound a sequence of four tones, and the "SNOW TEMP? C" prompt will appear. f. Collect the snow sample in the plastic scoop, noting the snow temperature (or ideally, have an assistant do it). Enter the snow temperature in degrees Celsius and press IR/S|. The "R/S WHEN ADD." prompt will appear. g. Open the calorimeter and dump the snow sample in. Press IR/S at the moment the snow sample is added to the freezing agent. The printer will print a record of the elapsed time when the snow sample was added in minutes and seconds and in seconds only. h. Close the calorimeter and shake the calorimeter vigorously to mix the freezing agent and snow sample thoroughly. Continue agitating the calorimeter as before. The temperature readings will begin 60-90 seconds after the snow sample was added, and the "<A> TO STOP" prompt will appear. i. When the temperature is again rising at a constant (or nearly constant) rate for 90-120 seconds, press [ to stop the automatic temperature recording. Stop agitating the calorimeter. The calculator will sound a sequence of four tones, and the "TOTAL MASS?" prompt will appear. j. Remove the lid of the calorimeter, making sure that no large pieces of ice cling to the temperature probe. Place the calor15

imeter (without the lid) on the electronic scale, and enter the mass (in grams) into the calculator and press IR/SI. The printer will print the mass of the snow sample, the mass of the freezing agent, and the temperature of the snow sample prior to being added to the calorimeter. The printer will then advance the paper several lines, and the program will stop. (Press IXEQ1, IALPHAj, [, [, [, [, |ALPHAj when ready to start the next measurement.) k. Pour the freezing agent/ice mixture through a filtering funnel into the wet oil container. Any ice remaining in the funnel may be discarded into a garbage bag. 1. Wipe the calorimeter lid and temperature probe dry with paper towels. Wipe the inside of the calorimeter dry using paper towels and the dish-washing tool. Several paper towels will be needed. Discard the used towels in the garbage bag. The average time for a complete measurement sequence, including cleanup, is 35-40 minutes. The fastest I have been able to complete the sequence is about 30 minutes, though I think this could be reduced slightly with an assistant. It is extremely difficult to maintain a 30-minute sampling rate without an assistant. Oil Recovery Most of the oil used as freezing agent can be recovered for re-use. A large portion of the ice in the oil can be removed by (1) allowing the wet oil container to warm up enough so that the ice particles melt and move to the bottom of the oil, (2) re-cooling the container so that the water layer re-freezes, and (3) pouring the oil into another container (the ice layer will be trapped in the original container, since it is too large to pass through the spout of the container). A second step, performed in the laboratory, removes small quantities of water and other particles by use of a separating funnel and careful pouring. The separating funnel is a glass funnel with a stopcock valve at the bottom. After allowing the wet oil to warm to room temperature and the water and other solids to collect at the bottom of the container, carefully pour some oil (which is on top) into the separating funnel. After inspecting the oil in the funnel visually, some or all can be added to the "dry oil" container or discarded, if water or other impurities are present. Do not try to pour all the oil layer out of the wet oil container-you will invariably get some of the water layer, too. Some of the oil will be lost, but it is better to lose some oil each time than to contaminate the freezing agent. 16

Data Reduction In order to use the formulas described earlier in this report, it is necessary to extrapolate the measured temperatures forward or backward to the time that the snow sample is added to the calorimeter. The assumption is that the heat transfer can be treated as if it occurred instantaneously; therefore, we need to determine the "initial" and "final" temperatures of the contents of the calorimeter, where "initial" and "final" refer to the instants just before and just after the snow sample is added. The temperature readings for a given measurement sequence are entered into a Cricket Graph6 data file along with the corresponding measurement times to produce a graph of temperature vs. time, as shown below: 240 - Snow added at 417 s 230 ----........... _..... E s _ Before After I. 220 E 1 210,. —* - 0 200 400 600 800 time (s) When the freezing agent or the snow sample is added to the calorimeter, the measured temperature changes suddenly and then approaches a linear increase. It is this linear temperature curve which we wish to extrapolate. To do this, the data points which indicate a linear trend (after the initial fluctuation) are copied into another column in the Cricket Graph data file and plotted. The Simple curve fit option is used to fit a line to these points. The coefficients associated with this line will be used in the next step in the data reduction. Typical plots are shown here (from file 8903020738): 6Copyright ~ 1986/87/88 Cricket Software. 17

225y = 218.55 + 7.5333e-3x R^2 = 1.000 223 * 221 5:3 22 1'-i~a^^ ^1" Before 219 * Before (corr) a. E o 217 215 - 0 100 200 300 time (s) 230 - y = 226.87 + 3.8254e-3x R^2 = 1.000 229 53 =~~~ 223~~~8-. ~B After * After (corr)!E * 227 226- ~, ~, ~ 400 500 600 700 time (s) Note that each measurement will have two line fits associated with it: a "before" and an "after" line. The three graphs (original, before, and after) are printed and retained for reference later. The extrapolated lines and resultant "initial" and "final" temperatures are shown below: 18

240 Snow added at 417 s Tf u Before 5., ^~_____ _~__ _*-________ — * After S_ -mI^ * Before (corr) jE 220 o After (corr) I. _..Ti 210-.,.,. 0 200 400 600 800 time (s) After performing the graphical portion of the data reduction, the masses, temperatures, and linear coefficients were entered into an Excel7 spreadsheet which was constructed using the formulas described previously. (A copy of the spreadsheet is included at the end of this report.) The spreadsheet calculates all intermediate results and the gravimetric snow liquid water content. By entering the snow density, the spreadsheet can also print the volumetric snow liquid water content. 7Microsoft ~ Excel, ~ 1985-1988 Microsoft Corp. 19

Excel spreadsheet for reduction of liquid water data 1 2 8 Date: 31087 T9 Tim (EST) 0.69166666666667 1 0 11.Data Set (YYMM D hh m m: 8902101636 13 Before Addin....Snow:____ 14 Interc -ept 230.1485 15 Slope 0.0072 17 After Adding S.now: 18 Intercepeot ---------— 235.9242 19 Slope 0.0045 20 21 Snow added at s): 439 22 2 3 Masses, (I):-__i..... 24 Freezing Agent (Oil) 356.5 25 Snow 47.2 26 2 7 Snow Temperature Ts (K 269 28 29 Tl (K)mb*x+bb 30 31 Tf =(K) ma*x+ba 32 33 TIf (K) (T.......i+Tf)/2 34 35 Tzf (K).(Tz+T)/2 36 37 Tsz (K) =(Ts+Tz)/2 38 39 Ts (K).(Ts+Tf)/2 40 41 Ts (~C) Ts-273.15 42 43 Ts > Tz? (1 = yes, 0 = no) -SIGN(SIGN TsCOtABSJSIGNffsC)) 45 Tsi Tz? 1 — e O no) ABSSIGN(SIGN TsC)-1_ 46 47. CoifIJ/ K).. ao Tif+bo —--- 47 _____________ 48 49 Cizt (cal/g K) =ai*Tzf+bi 50 Clzf (J/g K) IR[-R1C/cali 20

=1 |2 51 52 Cwsz cal/ K =aw*Tsz+bw 54 55 Clsf (cal/ K).ai*Tsf+bi 56 Cisf (J/g K) =R-11C/cali 57 58 basic [El Numerator (mo+E)*Coif*C -Ti)-hot*(msCizf*(Tz-Tf)cold*(ms*Cisf*(Ts-Tf) 59 60 basic Denominator d 60 baslc lE Denominator =ggms*(L+hot*(Cwsz*(Ts-Tz))-cold*(Cisf*(Ts-Tf))+cold*(Cizf*(z-Tf 61 62 Gray. Liquid Water Content: = Anum/Aden) 64 AT (K) =.TfT-Ti 65 66 Snow Te erature TC 67 68 Snow Densit g/cmA3)...^ not available 69 70 Vol. Liquid Water Content: =GLWC*rhos 6 7 3 Calories n a oule 0.23901 4 Freezing point of water (K) 273.15 5 Calorimeter Constant (g l 0) -- 80.344 6 Latent Heat of Fusion of Water J/ 333.458851 10 11 12 2 ___He Capacities: Constants for linear appn. (C=ax+b) 3 a b 4 Ice (cal/g K): 0.0019 -0.0082 5 Water (cal/g K): -0.0006038 1.1719 6 i0 (J/g K): 0.0011998 1.1871 21

Calorimeter Measurement Program for HP-41CX 1 i 2 1' LBL "TEMP" Calorimeter Program for HP41CX, Version of 28 January 1989. 2 FIX 5 Fix display of HP41 CX to five digits after decimal point. 3 AUTOIO Set HP-IL to auto mode. 4 "HP3468A" 5 FINDID Find HP-IL address of digital multimeter. 6 SELECT Select digital multimeter as primary device. 7 REMOTE Set digital multimeter to remote mode. 8 "N5" 9 OUTA Set display of multimeter to 5 digits. 10 "F4" 11 OUTA Set multimeter to 4-wire ohm measurement. 12 " — 14 --- 15 ACA 17 ACA 18 PRBUF Print dividing line at beginning of run. 19 RCLFLAG 20 STO 11 Store all flag settings in register 11. 21 0 22 ENTER^ 23 0B 24 BLDSPEC 25 0 26 BLDSPEC 27 6 28 BLDSPEC 29 1 9 36 BLDSPEC 31 9 32 BLDSPEC 33 - 6 34BLDSPEC 35 0 36 BLDSPEC 37 1 0 38 BLDSPEC "Build" special character (degree sign ) for printer. 39 STO 12 Store w" in register 12. 40 CLA Clear Alpha register. 41 8 42 XTOA 43 ]ASTO 10 Store "A" character in register 10. 44 CLA 45 - 40 46 XTOA Clear Alpha register. 47 ASTO 13 Store (" character in register 13. 48 CLA 49 41 50 XTOA Clear Alpha register. 22

_1 I 2 2 51 ASTO 14 Store ")" character in register 14. 5 2 CF00 5 3 SF 01 Set flag indicating 1st measurement (no AT wanted). 54 CF02 55 CF03 56 CF04 5 7 SF 27 Activate user keyboard. 5 8 STOPSW Stop stopwatch. 59 0 6 0 SETSW Set stopwatch to zero. 61 "EMPTY MASS?" 6 2 PROMPT Prompt for mass of empty calorimeter. 6 3 STO 06 Store empty mass in register 6. 6 4 "MASS W/OIL?" 6 5 PROMPT Prompt for mass of calorimeter + oil. 6 6STO 07 Store in register 7. 6 7 "R/S TO BEGIN" 6 8 PROMPT Prompt user to press R/S to begin measurement sequence. 6 9 TIME Recall time to X register. 7 0 RUNSW Start stopwatch. 71 STO 01 Store start time in register 1. 7 2 CLA Clear alpha register. 7 3 DATE Recall date to X register. 7 4 ADATE Append date to alpha register. 7 5 PRA Print date from alpha register. 7 6 CLA Clear alpha register. 7 7RCL 01 Recall start time from register 1. 7 8 FIX 4 Change to #.#### format (time will print as HH:MM:SS). 7 9 ATIME24 Recall start time to alpha register in 24-hour format. 8 0 FIX 5 Change to #.##### format. 81 PRA Print start time from alpha register. 8 2 ADV Advance printer one line. 83 "^AMEAS" Store name of control alarm (which measures cal. temp). 84 0.0015 8 5 ENTERA Enter repeat interval for control alarm (15 sec.) 86 0 8 7 ENTERA Enter date for control alarm (0 = today) 8 8 RCL 01 Recall start time from register 1. 8 9 0.0015 9 0 HMS+ Add 15 seconds to start time. 91 XYZALM Set control alarm for 15 sec. from start time. 92 LBL 00 1 9 3 "<A> TOADD" 9 4 CF21 Clear printer enable flag. 9 5 AVIEW Prompt user to press A when ready to add snow. 9 6SF21 Set printer enable flag. 9 7 ILB 01 98 0.2 9 9GETKEYX Return code of pressed key after 0.2 sec. 1 0 0FDN Put key code in X register. 23

* _ * l1| 2 102 X*Y? Was pressed key not the A key? 10 3 GTO 01 YES: Get another key code. 104 CLRALMS NO: Clear the control alarm, stopping the 15 sec. meas. 1 05 BEEP Sound a four-tone sequence. 10 6 "SNOW TEMP? C" 107 PROMPT Prompt user for snow temperature in ~C. 1 08 STO 04 Store snow temperature in register 4. 109 "R/S WHEN ADD." 1 1 0 PROMPT Prompt user to press R/S when snow is added to calorimeter. 1 I 1 RCLSW Get elapsed time when snow added. 1 2 STO 03 Store elapsed time in register 3. 113 ADV 1 14 ADV Advance printer 2 lines. 1 1 5 "SAMPLE ADDED AT 116 PRA Print alpha register. 1 17 CLA Clear alpha register. 1 1 8 FIX 5 Change to #.##### format. 119 ATIME24 Append elapsed time to alpha register in HH:MM:SS.s format. 1 20 PRA Print elapsed time. 121 HR Change elapsed time to decimal hours. 122 3600 123 * Convert elapsed time to seconds. 1 2 4 FIX 1 Change to #.# format. 1 25 CLA Clear alpha register. 1 26 ARCL X Append elapsed time to alpha register in #.# format. 1 2 7 "-" Append space to alpha register. 128 ACA Put alpha register in printer buffer. 129 115 130 ACCHR Append "s" to printer buffer. 11 31PRBUF Print printer buffer. 1 32 FIX 5 Change to #.##### format. 133 ADV 134 ADV Advance printer 2 lines. 1 35 TIME Put current time in X register. 1 3 6 RCL 01 Recall start time. 1 3 7 HMS- Subtract start time from current time. 1 38 HR Convert time difference to decimal hours. 139 240 1 40 * Convert time difference to quarter minutes. 141 2 142 + Add a half minute (2 quarter minutes). 1 43 INT Truncate decimal part to give integer number of quarter mins. 144: 240 14 S/ Convert result back to decimal hours. 146 HMS Convert to hours, minutes, seconds. 147 RCL01 1 4 8 HMS+ Add to start time. (Next meas. will be N*15 sec from start.) 149 0.0015 150 XoY Put repeat interval in Y register (15 sec.) 24

151 0 152 XoY Put date in Y register (0 = today). 1 53 "^^MEAS" Put name of control alarm in alpha register. 154 XYZALM Set control alarm. 1 5 "<A> TO STOP" 156 CF 21 Clear printer enable flag. 1 57 AVIEW Prompt user to press A when ready to stop. 158 SF 21 Set printer enable flag. 1 59 SF 01 Set flag indicating 1st measurement (no AT wanted). 160 LBL 08 161 0.2 162 GETKEYX Return code of pressed key after 0.2 sec. 163 RDN Put key code in X register. 164 11 1 65 X*Y? Was pressed key not the A key? 166 GTO 08 YES: Get another key code. 167 CLRALMS NO: Clear the control alarm, stopping the 15 sec. meas. 168 BEEP Sound a four-tone sequence. 169 "TOTAL MASS? 170 PROMPT Prompt user for total mass of calorimeter, oil, & snow. 1 71 RCL 07 1 72 - Subtract mass of calorimeter + oil. 173 1" M" 174 ARCL13 175 "-SNOW" 176 ARCL14 1771 "n=" Put" M(SNOW) -" in alpha register. 178 FIX 2 Change to #.## format. 1 79 ARCL X Append X register to alpha register. 180 ACA Put alpha register in printer buffer. 181. 32 1 82 ACCHR Append "" to printer buffer. 183 103 1 84 ACHR Append "g" to printer buffer. 185 PRBUF Print contents of printer buffer. 1 86 RCL 07 1 87 RCL 06 188 - Subtract mass of calorimeter from mass of calorimeter + oil. 189 "M" 190 ARCL13 1 91 "-FRZ AGr 192 ARCL14 1 9 3 "- Put "M(FRZ AGT) -" in alpha register. 1 94 -ARCLX Append X register to alpha register. 195 ACA Put alpha register in printer buffer. 196 32 1 97 ACCHR Append " to printer buffer. 1981 103 1 9 ACCHR Append "g" to printer buffer. 200 PRBUF Print contents of printer buffer. 25

II 1 7 2 — 201 "' 202 ARCL13 203 - SNOW" 204 ARCL14 2 0 5 "- " Put "T(SNOW) = " in alpha register. 20 6 FIX 1 Change to #.# format. 207 ARCL 04 Append snow temperature to alpha register. 208 "- " Append "" to alpha register. 209 ACA Put alpha register in printer buffer. 210 RCL12 211 ACSPEC Append "~" to printer buffer. 212 "C" 213 ACA Append "C" to printer buffer. 214 PRBUF Print contents of printer buffer. 215 " = " Put" =" in alpha register. 21 6 273.15 21 7 ST+ 04 Convert snow temperature from ~C to K. 21 8 ARCL 04 Append snow temperature (K) to alpha register. 219 "% K" Append " K" to alpha register. 220 PRA Print alpha register. 221 RCL 11 222 STOFLAG Reset flags to original status. 223 STOPSW Stop stopwatch. 224 0 225 SETSW Set stopwatch to zero. 2 26 LOCAL Set digital multimeter to local mode. 2 27 CLX Clear X register. 228 ADV 229 ADV 230 ADV 231 ADV 23 2 ADV Advance printer 5 lines. 2336 END 26

__1 | 2 1 LBL "MEAS " Measurement Subroutine for HP41CX, Version of 28 January 1989 2 RCLSW 3 STO 05 Store current elapsed time in register 5. 4 IND Input resistance value from digital multimeter. 5 TONE 7 Sound a tone. 6 RS 7 STO 22 Save Y register upon entry to subroutine in register 22. 8 R^ 9 STO 21 Save X register upon entry to subroutine in register 21. 10 RF 11 R * Restore resistance and time to X and Y registers. 1 2 STO 15 Store resistance in register 15. 13 ENTER* 1 4 ENTER* Duplicate resistance to Y and Z registers. 1 5.9902136 E-3 16* 17 2.360577 18 + 19* 20 27.19057 21 + Use 2nd degree polynomial to convert resistance to temp. 2 2STO 18 Store temperature (K) in register 18. 23 273.15 24 - Convert to ~C. 2 5 STO 17 Store temperature (~C) in register 17. 26 RCL18 27 RCL19 28 - Calculate difference between current and previous temps, AT. 2 9 STO 20 Store AT in register 20. 30 RCL18 31 STO 19 Store current temp. as previous temp. in register 19. 3 2 RCL 05 Recall time of measurement. 33 CLA Clear alpha register. 3 4 FIX 4 Change to #.#### format. 3 5 ATIME24 Place time of measurement in alpha register in HH:MM:SS fmt. 3 6 PRA Print alpha register. 3 7 HR Convert time of measurement to decimal hours. 3 8 3600 3 9 * Convert time of measurement to seconds. 4 0 FIX 0 Change to #. format 41 CLA Clear alpha register. 4 2 ARCL X Place time of measurement in alpha register (in seconds). 4 3 "-. " Append "" to alpha register. 4 4ACA Put alpha register in printer buffer. 45 115 4 6 ACCHR Append "s" to printer buffer. 4 7 PRBUF Print contents of printer buffer. 4 8 FIX 3 Change to #.### format. 4 9 "R *" Put "R " in alpha register. 50 ARCL 15 Append resistance value to alpha register in #.### format. 27

_1 2 51 "-~ ~'Append " to alpha register. ~52 ~ACA ~ Put alpha register in printer buffer. 53 17 54 AC~CHR Append "W" to printer buffer. ~55 ~PRBUF Print contents of printer buffer. ~56 FIX 2 Change to #.## format. ~57 ~T~ PPut "T " in alpha register. 58aARCL~ 17 Append temperature (~C) to alpha register. ~59 "-i" Append "" to alpha register. s6 0 ACA ~ Put alpha register in printer buffer. 61RCL 12 ~62 -ACSPEC Append "~" to printer buffer. 63 "C" ~64 ACA ~ Append "C" to printer buffer. ~65 PRBUF Print contents of printer buffer. 6 ~6 " 6 ~" Put" =" in alpha register. 67 ARCL 18 Append temperature (K) to alpha register. ~68^ r~K" Append " K" to alpha register. ~69 PRA Print alpha register. T7O~0 CLA Clear alpha register. 71 FI~X 2 Change to #.## format. 72 ARCL~ 1 0 Put "A" in alpha register. ~73 "-nT " ~ Append "T - "to alpha register. 74 ARCL 20 Append AT to alpha register. ~75" "K" ~ Append " K" to alpha register. 76FCC 01 -Is this not the first measurement? Clear the flag if set. ~77 PRA ~ YES: Print alpha register (containing AT) ~78 ~ADV Advance paper 1 line. 79 RCL22 8 0 RCL 21 Restore original X and Y registers. ~81 U3~END_28 28

Memory Map for Calorimeter Program MEMORY MAP Register Contents (italicized entries are used in MEAS.) 0 1 Start time. 2 3 Elapsed time when snow added. 4 Snow temperature, ~C 5 Current elapsed time (time of measurement). 6 Empty mass. 7 Mass of calorimeter + oil. 8 9 10 Delta "A" 11 Flag$ 12 Degree Sign " 13 14 15 Resistance value measured by multimeter 16 17 Measured temperature (~C) 18 Measured temperature (K) 19 Previous value of measured temperature (K). 20 AT (Tcurrent- Tprevious) 21 X register upon entry to MEAS routine 22 Y register upon entry to MEAS routine 29

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