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  4. An ideal gas is taken through the cycle A→ B→ C→ A, as shown in figure. If the net heat supplied to the gas in the cycle is 5 J, the work done by the gas in the process. C→ A is

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Q. An ideal gas is taken through the cycle $ A\to B\to C\to A, $ as shown in figure. If the net heat supplied to the gas in the cycle is $5 \,J$, the work done by the gas in the process. $ C\to A $ isPhysics Question Image

Rajasthan PMTRajasthan PMT 2007Thermodynamics

Solution:

Work done by gas is given by
$W=P \Delta V$
Total work done by gas is
image
$W=W_{A B}+W_{B C}+W_{C A} \ldots$(i)
From first law of thermodynamics
$\Delta Q =\Delta U+W \ldots$(ii)
Here $ W_{A B} =P \Delta V=10(2-1)=10 \,J $
$W_{B C} =P \Delta V=2 \times 0=0$
Hence, Eqs. (i) and (ii) will be written as
$5=0+\left(10+0+W_{C A}\right) $
$\Rightarrow W_{C A} =-5 J$