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  4. A thermal engine having three moles of mono-atomic gas as its working fluid undergoes the cyclic process as shown in the figure-3.87. Find the mechanical work over one cycle approximately (R = 8.314 J/mole-K) :

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Q. A thermal engine having three moles of mono-atomic gas as its working fluid undergoes the cyclic process as shown in the figure-3.87. Find the mechanical work over one cycle approximately $(R = 8.314\, J/mole-K)$ :Physics Question Image

Thermodynamics

Solution:

$W_{12} =W_{34}=0,$ (since the process is isochoric)
$W_{23} =P_{2}\left(V_{3}-V_{2}\right)=n R\left(T_{3}-T_{2}\right),$
$W_{41} =P_{1}\left(V_{2}-V_{4}\right)=n R T\left(T_{1}-T_{4}\right)$
$W =n R\left[T_{3}+T_{1}-T_{2}-T_{4}\right]$
$=3 \times(2400+400-1200-800)+8.314$
$\simeq 20\, kJ$