Heat and Thermodynamics 5 Question 20

21. An ideal gas expands isothermally from a volume V1 to V2 and then compressed to original volume V1 adiabatically. Initial pressure is p1 and final pressure is p3. The total work done is W. Then,

(2004, 2M)

(a) p3>p1,W>0

(b) p3<p1,W<0

(c) p3>p1,W<0

(d) p3=p1,W=0

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Solution:

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

In the graph, AB is isothermal and BC is adiabatic.

WAB= positive (as volume is increasing) 

and WBC= negative (as volume is decreasing) plus,

|WBC|>|WAB|, as area under p - V graph gives the work done.

Hence, WAB+WBC=W<0

From the graph itself, it is clear that p3>p1.

NOTE At point B, slope of adiabatic (process BC ) is greater than the slope of isothermal (process AB ).



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