Chapter 3, Problem 3.20CP

Interpretation Introduction

Interpretation:

Whether the given equation is only valid for an ideal gas at constant volume or not needs to be explained.

  ${\text{ΔU}}_{\text{v}}\text{= }{\displaystyle \underset{{\text{T}}_{\text{1}}}{\overset{{\text{T}}_{\text{2}}}{\int }}{\text{C}}_{\text{v}}\text{dT }}\text{= n}{\displaystyle \underset{{\text{T}}_{\text{1}}}{\overset{{\text{T}}_{\text{2}}}{\int }}{\text{C}}_{\text{v}}{\text{,}}_{\text{m}}\text{dT}}$

Concept Introduction : For an ideal gas, the internal energy is calculated as follows:

  ${\text{ΔU}}_{\text{v}}\text{= }{\displaystyle \underset{{\text{T}}_{\text{1}}}{\overset{{\text{T}}_{\text{2}}}{\int }}{\text{C}}_{\text{v}}\text{dT }}$

Here U is the internal energy, T is the temperature, n is the number of moles and C_vis the heat capacity a constant volume.