Specific Heat of substances. Calorimetry
General characteristic of the calorimetric methods for the measurement of specific heat
The methods discussed here and the instruments for their execution have been selected arbitrarily from an immense pool of other or similar offerings. The student should only gain an impression of the general foundations of calorimetry. The necessity of the measurement of quantities of heat arises during the treatment of manifold tasks, not only during the measurement of specific heat. For example, during the determination of the heats of melting, evaporation, combustion, absorption of gases and the heat tone of chemical processes, etc.
In order to determine the quantity of heat, which a body demands, in order to raise its temperature by 1ºC, you either supply it with heat to a given temperature t1º and let it then pass on heat in a calorimeter until it has cooled down to a temperature t2º or you heat it by means of a given amount of heat and measure the corresponding rise in temperature.
If the amount of heat, which the body lost during cooling from t1º to t2º, is as large as what it required during heating from t2º to t1º? Yes - assuming that the body while it was cooling passed during downwards heating through the same changes which it experienced during upwards heating (this follows from the second main theorem). We will assume that this is so. The heat, which is lost during the process in the calorimeter, serves in the one method to melt ice (mixing method), in the other method to heat water. You measure in the first method the number of grams of ice melted, in the second by how many degrees the temperature of a given mass of water has risen, during the loss of which the body cooled by several degrees, measured by a thermometer. If the specific heat at every temperature is the same (as with mercury and almost with water), then the calorimetricly determined specific heat is the true - the specific heat at a temperature; however, if it depends on the temperature, then it is the mean specific heat.
Ice melting method
In the set-up of this method of Lavoisier the calorimeter consists of three sheet iron vessels (Fig.393) which enclose each other. The innermost, the sieve like vessel M, contains the body, heated to the given temperature t10, which is to pass its heat on to its environment and melt ice; the central one, A, contains ice; the outer one, B, protects the ice, which after all is only to accept heat from the body inside, from any heat coming from outside and is therefore likewise filled with ice. While heat from outside melts the ice in B, it cannot raise the temperature of B beyond zero before not all ice in B has melted and therefore also not act on the ice in A; as a consequence, the environment of the body M remains at zero temperature and the body cools down from its initial temperature t10 to 0º. You weigh the melting water, which drains at D, and since you know from other measurements, that 79.67 cal are required to melt 1 gram of ice, you find the amount of heat given off by the body, in order to yield the weighted amount of melt water during the reduction of its temperature from t10. - This (old fashioned) method is not exact, because the melting water sticks partly to the ice.
The ice calorimeter of Bunsen avoids this defect of Lavoisier's method.He finds the number of melted grams of ice by measuring volumes. 1 g of ice occupies 1.0908 cm³, 1 g of water 1.0001 cm³. Hence, as ice melts, it reduces its volume by 0.0907 cm³. The measured reduction in volume of melting ice indicates the number of grams which have melted. Fig. 394 shows the instrument, completely blown out of glass. The U-tube C, the wider part g of which ends above in a small test tube A for the body to be examined, contains above b water and ice (as a kind of a coat hanging on to A), mercury from b into the calibrated capillary S . The instrument has protection against external heat effects by being surrounded by a mixture of ice and water. You place the body, heated to tº, into the tube filled with water at temperature 0º. The body passes its heat to the water and through it to the ice; the ice melts, the volume occupied by ice and water reduces and allows the mercury to rise above b. The displacement of the mercury column in S indicates the number of cm³, which have risen above b. 11.03 g of melted ice correspond to a volume change of 1 cm³. - The Bunsen calorimeter allows to make very exact measurements and requires only a few grams of the substance to be investigated, but demands strict conformity with several intricate rules (for example, for the production of the ice mantle).
If you employ the heat from the test body for heating water, you dip the body, heated to a given temperature, into a measured quantity of water at a given temperature and measure the water's change of temperature. Therefore the water calorimeter of Regnault 1840 has two parts (Fig. 395): A chamber B, heated by steam, which heats the test body A (in a little basket) and the actual calorimeter vessel D, into the water of which you dip the body afterwards. dd is an isolating water layer between B and D. If the body has at first the temperature t10 and the water the (lower) temperature t20, the body loses heat to the water until both have the same temperature. The water has then heated up by (t3 - t2)º, the body cooled down by (t1 - t3)º. If m g is the amount of water, it has taken in m(t3 - t2) cal (every gram for every degree temperature rise 1 cal). The water has received this heat from the body, whence , if it cools by (t1 - t3)º, it loses (t3 - t2) cal. Therefore it must take in the same amount of heat, in order to heat up by (t1 - t3)º. If the mass of the body is M g, the observation yields: In order to heat M g of the body by (t1 - t3)º, you require m(t3 - t2) cal; in order to heat up 1 g of it by 1º, you need [m(t3-t2)]/[M(t1-t3) cal. This number is its specific heat.
The walls of the vessels and the thermometer also heat up and heat is lost by heat exchange of the calorimeter with its environment, In order to correct for this, you must discover the water values of the calorimeter and of the thermometer; you must also allow for the loss of heat to the outside.
The above expression for the specific heat also yields the mixing temperature x, if you measure different quantities of water at different temperatures with each other. Imagine that the test body has been replaced by water. Since the specific heat of water is 1 and the temperature, previously denoted by t3, is now the unknown mixing temperature x, you have the equation
1 = [m(x - t2)]/[M(t1 - x) or x = (Mt1 + mt2)/(M + n) degree.
For example, if you mix 10 g water at 30º with 8 g water at 20º, you obtain 18 g water at
x = [10·30 + 8·20]/[10 + 8] = 25.5º.
This is Richmann's Rule. It is generally applicable to mixing of substances of equal specific weight.
Metal block calorimeter for measurement of specific heat at very low temperature (Nernst 1911)
In order to measure the specific heat at very low temperatures, you heat the substance electrically as a massive block (worse conducting substances in an air tight silver container filled with hydrogen) by a thin platinum wire. You compute the introduced heat using the current intensity and the resistance of the wire. After turning off the heating, the wire serves as a very sensitive resistance thermometer for the determination of the increase in temperature. During the measurement, the substance of the filled silver container hangs in a well evacuated glass container (Fig. 396), which is surrounded by liquid air or liquid hydrogen. The absence of a gas, that is, also of heat convection and the complete absence of radiation at the deep temperature allows very exact measurements of the true (not mean!) specific heat. - At higher temperatures, Nernst employed a copper calorimeter (Fig. 397), made out of a block weighing about 400 g, which has a long hole for the substance. Good heat conductivity gives the copper block K the same temperature everywhere. In order to remove heat from the environment, it is installed in the Dewar container D.
Measurement of the specific heat of gases
While you can determine cv experimentally, it is in most cases simpler to find cp. The theory yields cp - cv as well as cp/cv, whence cv can be computed. Formerly (Regnault), in order to measure cp, a measured quantity of the gas was first heated to a given starting temperature - fed it through a spiral tube inside a water calorimeter.The volume of the gas, its initial and final temperature and the increase in temperature of the calorimeter water yield then cp.
Just as exact as the best other methods, possibly even superior to them (Eucken) is the method of stationary, electrically heated gas flow (applied in the principle of Callendar for the measurement of the specific heat of fluids, 1902). At the present time (1935), precision measurements were done by it: In the flow of gas lies an electrical heater, protected against loss of heat,. The temperature is determined just ahead of it and just behind it by means of a platinum thermometer. The temperature difference, the gas velocity (cm³/sec) and the electrical performance yield directly cp. Fig. 398 shows the instrument, made (apart from the heating element H) out of glass. A, B, C are protective covers against heat loss, P1 and P2 thermometers. The bounds between which the instrument has been employed hitherto (1935) are - 180ºC (Scheel) and 500ºC (Haber). At room temperature and 1 atm, cp has the values:
The fraction cp/cv = k can be determined by simple methods on the basis of theoretical considerations. For air, the velocity of sound yields k = 1.40 and approximately the same result follows from measurements by means of an experimental method due to Clément and Charles Bernhard Désormes 1819. Their specific heat at constant volume is thus: 2.41/cv = 1.40, that is, cv = 0.172, that is, it is considerably smaller than at constant pressure. The value of k for oxygen, hydrogen and nitrogen agrees almost with that for air, that for composite gases deviates considerably. For example, k has the values:
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