Question

A cycle followed by an engine (made of one mole of an ideal gas in a cylinder with a piston) is shown in figure.

The heat exchanged by the engine with the surroundings at constant volume is (Take CV = $\frac { 3 } { 2 }$ R)

• A. (PB – PA)VA
• B. $\frac { 1 } { 2 }$(PB – PA)VA
• C. $\frac { 3 } { 2 }$ (PB – PA)VA
• D. $\frac { 5 } { 2 }$(PB – PA)VA

Answer 1

Answer: (C)

$\frac { 3 } { 2 }$ (PB – PA)VA

Answer 2

:

In the given figure, portion AB of the cycle shows increase in pressure/ temperature of gas at constant volume.

Therefore system gains the from the surroundings, then

$Q _ { A B } = U _ { A B } = n C _ { v } \Delta T$ $Q _ { A B } = 1 \times C _ { V } \times \Delta T = \frac { 3 } { 2 } R \left( T _ { B } - T _ { A } \right) = \frac { 3 } { 2 } \left( P _ { B } V _ { B } - P _ { A } V _ { A } \right)$ $\therefore Q _ { A B } = \frac { 3 } { 2 } \left( P _ { B } - P _ { A } \right) V _ { A } \left( \because V _ { A } = V _ { B } \right)$