Question

The state of a mole of an ideal gas changed from state A($2p,v$) through four different processes and finally return to initial state A reversibly as shown below.

Calculate the total work done by the system and heat absorbed by the system in the cyclic process respectively.

• A. $-pv,pv$
• B. $-2pv,2pv$
• C. $pv,-pv$
• D. $2pv,-2pv$

Answer 1

The correct option is A $-pv,pv$

State A to State B (Isobaric expansion):
Pressure is held constant at $2p$ and the gas is heated until the volume $v$ becomes $2v$.
$\therefore w_1=-p\Delta V=-2p(2v-v)=-2pv(=areaABFE)$

State B to State C (Isochoric process):
Volume is held constant at $2v$ and the gas is cooled until the pressure $2p$ reaches $p$
$\therefore w_2=0since\Delta V=0$

State C to State D (Isobaric compression):
Pressure is held constant at $p$ and the gas is further cooled until the volume $2v$ becomes $v$
$\therefore w_3=-2p(v-2v)=pv(=areaCDEF)$

State D to State A (Isochoric process):
Volume is held constant at $v$ and the gas is heated until the pressure $p$ reaches $2p$
$\therefore w_4=0since\Delta V=0$
total work done by the gas $w=w_1+w_2+w_3+w_4$
$w=-2pv+0+pv+0$
$w=-pv(=areaABCD)$
as the process is cyclic $\Delta U=0$
$q=\Delta U-w$
$q=0-w$
$q=pv$
where q is heat absorbed in the cyclic process