Chapter 15, Problem 61GP

(a)

To determine

The work done by the ideal gas for path ADC.

Answer to Problem 61GP

The work done by the ideal gas for path ADCis $P_A\left(V_C-V_A\right)$ .

Explanation of Solution

Given info:

The pressure for the state A and D is, $P_1=P_A=P_D$

The pressure for the state B and C is, $P_2=P_B=P_C$

The volume for the state A and B is, $V_1=V_A=V_B$

The volume for the state C and D is, $V_2=V_C=V_D$

Formula Used:

The expression to calculate the work done by the ideal gas for path ADCis,

  $W_{ADC}=P_1\left(V_2-V_1\right)$

Calculation:

Substitute all the values in the above expression.

  $W_{ADC}=P_A\left(V_C-V_A\right)$

Conclusion:

Thus, the work done by the ideal gas for path ADCis $P_A\left(V_C-V_A\right)$ .

(b)

To determine

The work done by the ideal gas for path ABC.

Answer to Problem 61GP

The work done by the ideal gas for path ABCis $P_B\left(V_C-V_B\right)$ .

Explanation of Solution

Formula Used:

The expression to calculate the work done by the ideal gas for path ABCis,

  $W_{ABC}=P_2\left(V_2-V_1\right)$

Calculation:

Substitute all the values in the above expression.

  $W_{ABC}=P_B\left(V_C-V_B\right)$

Conclusion:

Thus, the work done by the ideal gas for path ABCis $P_B\left(V_C-V_B\right)$ .

(c)

To determine

The work done by the ideal gas for path AC.

Answer to Problem 61GP

The work done by the ideal gas for path ACis $\frac{1}{2}\left(P_A+P_C\right)\left(V_C-V_A\right)$ .

Explanation of Solution

Formula Used:

The expression to calculate the work done by the ideal gas for path ACis,

  $W_{AC}=\frac{1}{2}\left(P_1+P_2\right)\left(V_2-V_1\right)$

Calculation:

Substitute all the values in the above expression.

  $W_{AC}=\frac{1}{2}\left(P_A+P_C\right)\left(V_C-V_A\right)$

Conclusion:

Thus, the work done by the ideal gas for path ACis $\frac{1}{2}\left(P_A+P_C\right)\left(V_C-V_A\right)$ .