Question

Six moles of an ideal gas performs a cycle shown in the figure. If the temperature is $T_A=600K$ , $T_B=800K$ , $T_C=2200K$ and $T_D=1200K$ , the work done per cycle is

• A. $20kJ$
• B. $30kJ$
• C. $40kJ$
• D. $60kJ$

Answer 1

Answer: (C)

$A\to B$ and $C\to D$
$V=$ constant $W_{AB}=W_{CD}=0$
$W_{BC}=P\Delta V$
$W_{BC}=nR{\left(\Delta T\right)}_{BC}$
$W_{DA}=nR{\left(\Delta T\right)}_{DA}$
Total work done in a complete cycle
$W_{total}=W_{AB}+W_{BC}+W_{CD}+W_{DA}$
$W_{total}=0+W_{BC}+0+W_{DA}$
$W_{total}=0+nR{\left(\Delta T\right)}_{BC}+0+nR{\left(\Delta T\right)}_{DA}$
$W_{total}=nR\left(T_C-T_B+T_A-T_D\right)$
$W_{total}=40kJ$