Chapter 5, Problem 1P

To determine

The case for which the done is greater for an ideal gas which expands to a fixed volume at constant pressure then at constant temperature.

Explanation of Solution

The boundary work which is equal to $Pd\nu$ is described under the process curve of $P-\nu$ diagram for the quasi-equilibrium process.

The equation of area under the process curve of $P-\nu$ diagram is,

  $\begin{array}{c}\text{Area under the curve}={\displaystyle \underset{1}{\overset{2}{\int }}dA}\\ W={\displaystyle \underset{1}{\overset{2}{\int }}Pd\nu }\end{array}$

Here, pressure is P, change in the volume is $d\nu$, and change in the area is $dA$.

From above equation, the constant pressure case had a greater work done.