Question

The value of the heat capacity for a substance depends on whether it’s measured under constant pressure conditions or constant volume conditions. The constant-pressure molar heat capacity is given by

$\overline{Cp}$ = (dq/dT)_P

and the constant-volume heat capacity is given by

$\overline{Cv}$ = (dq/dT)_V

Note that we use d instead of $\partial$ because q is not a state function of temperature, volume, and pressure; its value depends on how we execute the process.

Here are several questions regarding heat capacity.

a. When we heat a substance, such as a gas, at constant pressure, does its volume increase, decrease, or remain the same? Is w positive, negative, or zero?

b. When we heat a substance, such as a gas, at constant volume, does its volume increase, decrease, or remain the same? Is w positive, negative, or zero?

c. We transfer the same amount of thermal energy into a gas under constant pressure, and constant volume conditions. Which set of conditions results in a greater change in the temperature of the gas?

d. Explain why a-c imply that the constant-pressure heat capacity for any substance is larger than the constant-volume heat capacity.

Answer 1

a. Volume increases. Work done is negative.

b. Volume remains the same. Work done is zero.

c. The change in temperature shall be more for the system with constant volume because the entire heat energy supplied contributes to the change in temperature as the work done is zero.

d. The constant-pressure heat capacity for any substance is larger than the constant-volume heat capacity because of the non-zero work for an isobaric process as compared to the zero work for isochoric process.