Chapter 3, Problem 3.30P

Interpretation Introduction

Interpretation:

To find the values of $Q$, $W$, $\Delta U$ and $\Delta H$ for a process in which one mole of air initially at ${\text{150}}^{\text{o}}\text{C}$ and $8\text{bar}$ expands mechanically reversible isothermally such that when it is cooled at constant volume to ${\text{50}}^{\text{o}}\text{C}$ its final pressure become $3\text{bar}$ . Assume air is an ideal gas and the values of specific heats are $C_P=\frac{\text{7}}{\text{2}}\text{R}$, $C_V=\frac{5}{\text{2}}\text{R}$ .

Concept Introduction:

The total amount of $Q$, $W$, $\Delta U$ and $\Delta H$ would be calculated using individual value of both process isothermal followed by constant pressure. So, for these types of problem we usually calculate value for each process and then add them to find total value of path.

For isothermal expansionprocess,

  $PV=\text{constant}$

And

  $W=nR{T}_1\ln (\frac{V_2}{V_1})$

  $\Delta U=0$

  $Q=W=nR{T}_1\ln (\frac{V_2}{V_1})$

  $\Delta H=n{C}_P(T_2-T_1)=0$

For constant volume process,

  $\frac{P_1}{T_1}=\frac{P_2}{T_2}$

And

  $W=0$

  $\Delta U=n{C}_V(T_2-T_1)$

  $Q=\Delta U$

  $\Delta H=n{C}_P(T_2-T_1)$