Heat Capacity Ratio
المؤلف:
Sidney B. Cahn, Gerald D. Mahan And Boris E. Nadgorny
المصدر:
A GUIDE TO PHYSICS PROBLEMS
الجزء والصفحة:
part 2 , p 17
29-8-2016
1549
Heat Capacity Ratio
To find CP/CV of a gas, one sometimes uses the following method. A certain amount of gas with initial temperature T0, pressure P0, and volume V0, is heated by a current flowing through a platinum wire for a time t. The experiment is done twice: first at a constant volume V0 with the pressure changing from P0 to P1, and then at a constant pressure with the volume changing from V0 to V1 The time t is the same in both experiments. Find the ratio CP/CV (the gas may be considered ideal).
SOLUTION
If the gas is heated at constant volume, then the amount of heat Q transferred to the gas is
(1)
where cv is the heat capacity by weight of the gas, m is the mass, and T is the temperature at pressure P1. Using the ideal gas law at the beginning and end of heating gives
(2)
where n is the number of moles of the gas. From (1) and (2),
(3)
and
(4)
For heating at constant pressure,
(5)
Similarly,
(6)
So
(7)
and
(8)
Since the time t during which the current flows through the wire is the same in both experiments, the amount of heat transferred to the gas is also the same: Q' = Q. Equating (4) and (8), we obtain
(9)
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