# Derive and Apply Heat Capacity

Suppose that the enthalpy of some substance over a large temperature range can be expressed as a function of the temperature (where alpha, beta and gamma are constants):

H =alpha*ln(T) + ln(gamma) + beta/T^2

a) What is the heat capacity of this substance at constant pressure?

b) You begin with two samples each containing 1 mole of a dilute monatomic gas. One sample (sample A) is kept at constant pressure and the other sample (sample B) is kept at constant volume. Both gas samples are at the same temperature. You now add 3 kJ of energy through heat exchange to both gas samples. What will be the difference in the temperature between the two samples?

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#### Solution Preview

"Suppose that the enthalpy of some substance over a large temperature range can be

expressed as a function of the temperature (where alpha, beta and gamma are constants):

H =alpha*ln(T) + ln(gamma) + beta/T^2

a) What is the heat capacity of this substance at constant pressure?

b) You begin with two samples ...

#### Solution Summary

This solution contains explanations for two problems. First, the heat capacity of a substance is derived using thermodynamic principles and a given equation for enthalpy. Second, heat capacities of monatomic gases at constant pressure and constant volume are used to calculate the temperature change for each with an increase in internal energy.