An ideal gas expands isothermally from a volume V₁ to V₂ and then compressed to original volumes V₁ adiabatically. Initial pressure is p₁ and final pressure is p_3.The total work done is W. Then,
Select one:

Question

a)
p₃= p₁ , W = 0
b)
p₃> p_{1, W < 0}
c)
p₃ < p_{1, W < 0}
d)
p₃ > p_{1, W > 0}

Correct answer is option 'B'. Can you explain this answer?

Answer

Slope of adiabatic process at a given state (p, V, T) is more than the slope of isothermal process. The corresponding p-V graph for the two process is as shown in figure.

In the graph, AB is isothermal and BC is adiabatic.
W_AB is positive (as volume is increasing)
and W_BC is negative (as volume is decreasing)

as area under p–V graph gives the work done.
Hence,

From the graph itself, it is clear that p₃ > p₁
The correct answer is: p₃> p₁ , W < 0

Answer

= p1 , W < />
c)p3 > p1 , W > 0
d)p3 > p1 , W < 0='' />

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