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Question

In a cyclic thermodynamic process, an ideal gas is first compressed at constant volume while its internal energy is increased by 350 J. Then it expands adiabatically until it returns to its original pressure. Finally, the gas is returned isobarically to its original state when 60.0 J of work is performed on the gas while its internal energy decreases by 200J. If the change in internal energy (in 𝑆𝐼 𝑢𝑛𝑖𝑡) during the adiabatic expansion is X, then find the value of (X+500).Assume the gas is ideal with CP=20.8JmolK and Cv=12.5JmolK.

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Solution

Given, change in internal energy during isochoric compression,
U12=350J

Work done on the gas during isobaric compression,
W31=60J

And internal energy decreases during isobaric compression,
U31=200J

Let initial internal energy of the gas be U1.
So,

U2=U1+350(i)

U3=U1+200(ii)

So, change in internal energy during adiabatic expansion,
U23=X=U3U2=150

So,X+500=(150+500)=350

Final answer: (350)

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