Chapter 7, Problem 127FP

Interpretation Introduction

(a)

Interpretation:

The value of heat capacity $C_v$ at constant volume for 1 mol of gas needs to be determined.

Concept introduction:

The average translation kinetic energy of gas molecules is defined by the equation:

$\overline{e_{\text{k}}}=\frac{3}{2}\left(\frac{RT}{N_{\text{A}}}\right)$

Here, R is gas constant, T is temperature, and N_A is Avogadro’s constant.

Also, the internal energy for heating of N molecules of an ideal gas is proportional to the average translation kinetic energy of gas molecules:

$U=N\overline{e_{\text{k}}}$

Interpretation Introduction

(b)

Interpretation:

The value of heat capacity $C_p$ at constant pressure for 1 mol of gas needs to be determined.

Concept introduction:

In a constant pressure heating of an ideal gas, change in enthalpy is defined as:

$\Delta H=\Delta U+nR\Delta T$

Also, the heat of a process at constant pressure is equal to change in enthalpy. Then from first law of thermodynamics, change in enthalpy is defined as:

$\Delta H=q$