Chapter 3, Problem 3.1CYU

The paths ABC, AC, and ADC represent three different quasi-static transitions between the equilibrium states A and C .

Check Your Understanding How much work is done by gas, as given in Figure 3.6, when it expands quasi-statically along the path ADC?

To determine

The work done by the gas when it expands quasi-statically along the path ADC.

Answer to Problem 3.1CYU

The work done by the gas when it expands quasi-statically along the path ADC is $p_2\left(V_2-V_1\right)$.

Explanation of Solution

Formula Used:

The work done by the gas when it expands quasi-statically along the path ADC is given by:

  $W={\displaystyle {\int }_{V_1}^{V_2}pdV}$

Calculation:

The work done by the gas when it expands quasi-statically along the path ADC is calculated as,

  $\begin{array}{c}W={\displaystyle {\int }_{V_1}^{V_2}pdV}\\ =p_2{\displaystyle {\int }_{V_1}^{V_2}dV}\\ =p_2{\left[1\right]}_{V_1}^{V_2}\\ =p_2\left(V_2-V_1\right)\end{array}$

Conclusion:

Therefore, the work done by the gas when it expands quasi-statically along the path ADC is $p_2\left(V_2-V_1\right)$.