In elementary physical chemistry courses the heat capacities of gases are a topic which can be discussed from a kinetic theory viewpoint. Unfortunately, there are few laboratory experiments which allow a direct determination of the heat capacities of gases and therefore an experimental verification of some of the results of kinetic theory. This article describes a simple flow calorimeter that can be con- structed from materials that are available from chemi- cal supply houses. The calorimeter in this form gives heat capacities which deviate from the accepted values by *3%. The experimental results can be compared with the predictions of kinetic theory and hence integrated into the results of elementary lecture courses in physical chemistry. Furthermore with the growing interest in high temperature phenomena, flow measurements are again of interest. The method of treatment of the data shows the student how heat losses in calorimetric measurements can be taken into account in calculations.

Figure 1 is a diagram of the calorimeter. The outer jacket is the outer tube for a hydrogen electrode as- sembly. The two thermometers can be read to 0.2 degree. The heater is made of Nichrome wire (BS 29)

Percy E. Pierce Case Institute of Technology

Cleveland, Ohio

HEATER

- # A 0

INLET TIERYOMETER

A Simple Flow Calorimeter

Figure 1. The Row calorirneler.

INLET

wound on a plastic cross; it has a resistance of 5 4 ohms. Auxiliary equipment to maintain a steady gas flow and to control the heat input to the heater are required. These will be discussed later. Gas enters the inlet a t a steady rate and passes over the heater, whose rate of power dissipation is held constant. A steady state is established in the system when the inlet and outlet thermometers attain constant readings.

The heat dissipated by the heater is partly taken up by the gas flowing over the heater and partly lost to the surroundings of the apparatus according to the following equation':

Q = GATR + L (1)

where

Q = EI = rate of heat production in the resistor, cp = the mean heat capacity of the gas over the temperature interval AT,

AT = the temperature change of the gas flowing over the heater,

R = the rate of flow of the ges, and L = the rate of heat loss to the surroundings.

Since AT is small, the heat losses t,o the surroundings are proportional to AT

= KAT (2)

The factor K is determined by the thermal characteris- tics of the materials that make up the calorimeter and the geometry of the apparatus. The heat balance equation becomes

Q = ?*ATR + KAT (3)

If we divide equation (3) by AT we obtain

&/AT = C n ~ + K (4)

If we determine Q and AT at various flow rates and plot Q/AT against R, the slope of the straight line obtained will be the mean heat capacity of the gas. I t is necessary to keep AT the same for all measure- ments if €* varies greatly with temperature.

The dot notation used here designate the variation of the quantity with time. Thus Q = dQldt.

rigwe 2. ~ i o t of Oj-\~verrur k far nitrogen gar

338 / Journol of Chemical Education

Figure 2 shows a plot of Q/AT versus R for nitrogen gas. Typical student results for C,, (cal/mole) ranged from 6.50 to 7.25, with an average of 6.92; u = 0.21; u/<C,> X 100 = 3%. Theinitial temperaturesvaried from 25 to 27°C; the final temperatures varied from 35 to 41°C.

The major source of error in the experiment is in not waiting a sufficient length of time for the calorimeter to attain a steady state; 10-15 minutes are required for each point. A AT of 10°C has been found to yield satisfactory results with nitrogen.

An alternate scheme for calculating C, is to divide equation (4) by R.

@ATR = C9 + K I R ( 5 )

The quantity Q/ATR is the apparent heat capacity of the gas if we neglect heat lossqs. If we plot this apparent heat capacity versus 1/R and extrapolate to 1/R = 0 (i.e., infinite flow rate) the intercept of the straight line obtained is the true heat capacity. This method has been employed by Pitzere to calculate the heat capacity of vapors. Figure 3 shows a plot of Q/AT R versus 1/R for nitrogen. The first method of calculation has been found the more suitable with the apparatus described, since the heat losses to the surroundings are rather large.

Figure 3. Plot of lhe apparent heat caposity of nitrogen versus 1IR.

The heater circuit is shown in Figure 4. An Edison cell is used as a source of power. The voltage is con- trolled by a slide wire rheostat. The voltage is ad- justed to about 3 v and a current of 0.5 amps results. In practice the heater circuit is so stable that it re- quires virtually no adjustment during the course of a determination.

Figure 5 shows the gas train. The gas is fed from a cylinder through a pressure regulator and needle valve into the gas circuit. A two-stage pressure re- duction from the cylinder results in more constant flow rates. The pressure of the gas in the second stage should he adjusted to about 10 psi. The gas flows into a surge tank of 6-8 liter capacity to further reduce fluctuations in eas flow. The flow meter used was of

BATTERY RHEOSTAT

Figure 4. The heater sircult.

the orifice type and was calibrated using a wet test meter. The students are supplied with a calibration curve for the flowmeter. The flow rate is held con- stant during the experiment by manually adjusting the diaphragm valve on the pressure regulator. This step is important and generdly requires some attention since the flow has a tendency to drift slightly during the course of a determination.

Procedure

The flow of gas through the calorimeter is adjusted and maintained a t a constant value. The heater is turned on and the rheostat is adjusted so that the volt- age is in the range 2.3-2.9 volts. The apparatus is allowed to warm up. This should take about 5 minutes. The rheostat is adjusted so that for the given flow rate the difference between inlet and outlet temperature is approximately 10°C. It is necessary to make minor adjustments of the flow rate as the experiment proceeds. After about 10-15 minutes the apparatus will have achieved a steady state. The voltage, current, tem- peratures of the inlet and outlet thermometers, and flow rate are recorded. The above procedure is re- peated at five different flow rates.

From the data, Q in calories per second and R in moles per second are calculated. A plot of Q/AT against R yields a straight line whose slope is Cn in cal/ mole dcg.

' PITIER, K. S., J. Am. Chem. Soc., 63, 2413 (1941). Figure 5. The gar flow system.

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Volume 39, Number 7, July 1962 / 339