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 for path D to A is (at constant pressure)

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

Answer 1

Answer: (B)

$\frac { 5 } { 2 }$ PA(VA – VD)

Answer 2

: since DA involves compressing of gas from $V _ { A }$at constant pressure $P _ { A }$. The work will be done on gas.

$\therefore Q _ { D A } = U _ { D A } + W _ { D A }$ $= \frac { 3 } { 2 } \left( P _ { A } V _ { A } - P _ { D } V _ { D } \right) + P _ { A } \left( V _ { A } - V _ { D } \right)$ $= \frac { 3 } { 2 } P _ { A } \left( V _ { A } - V _ { D } \right) + P _ { A } \left( V _ { A } - V _ { D } \right) \left( \because P _ { A } = P _ { D } \right)$

$= - \frac { 5 } { 2 } P _ { A } \left( V _ { D } - V _ { A } \right) = \frac { 5 } { 2 } P _ { A } \left( V _ { A } - V _ { D } \right)$