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Q.

The figure shows the  p-V plot of an ideal gas taken through a cycle ABCDA. The part ABC is a semi-circle and CDA is half of an ellipse Then, 

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a

The process during the path AB  is isothermal 

b

Work done during the path ABC is zero 

c

Heat flows out of the gas during the path  BCD.

d

Positive work is done by the gas in the cycle ABCDA.

answer is B, D.

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Detailed Solution

The process  A  B lies on a circle having centre  (2, 2)  and radius 1 unit. The  equation of the circle is given by   (p2)2+(V2)2=1
 The ideal gas equation is  pV=nRT. The product  pV not constant in the process AB  and   hence the process is not isothermal .  
 In the process  B  CD the product  pV decreases from 6 units to a value less than 2 units  Thus, the temperature of the gas reduces in this process.  Hence, internal energy of the gas decreases i.e.,  ΔU<0.  Also, work done by the gas is negative, ΔW<0 (since  volume decreases ) . Substitute in the first law of thermodynamics,  ΔQ=  ΔU+ΔW, to get  ΔQ<0 The  negative sign of  ΔQ indicates  heat flows  out of the gas. The  Work done by the gas is given by area under the  p-V diagram, It is positive for the process  AB (volume increases) and negative for the process BC  (volume decreases). The magnitude of area under AB is more than area under BC. Note that,
   WAB=2+π/2 
 WBC=(1+π/2) 
  WABC=WAB+WBC=1
Thus, the work is done by the gas in the process ABC  as  WABC>0.
Using the same argument for the cycle ABCDA, positive work is done by the gas in this cycle. This work  is equal to the area enclosed by the curve ABCDA . 

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