Chapter 3, Problem 3.18P

Interpretation Introduction

Interpretation:

When 1 mole of an ideal gas expands by each of the isochoric, isothermal and adiabatic paths, $W$, $Q$, $\Delta U$ and $\Delta H$ should be calculated for each path assuming mechanical reversibility.

Concept introduction:

The formula at constant volume is given by:

$\begin{array}{l}{P}_{1}V=nR{T}_1\\ P_{2}V=nR{T}_2\Rightarrow \frac{P_1}{P_2}=\frac{T_1}{T_2}\end{array}$

The formula at constant temperature is:

$\Delta U=C_V\Delta T$

$\Delta H=C_P\Delta T$

When, $\Delta T=0$, $\Delta U=\Delta H=0$

Hence, by the first law of thermodynamics,

$\begin{array}{l}\Delta U=0=Q-W\\ Q=W\end{array}$

Now, in adiabatic process, there is no change in heat occurs i.e.

$Q=0$