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Q.

One mole of a monatomic gas is taken  through a cycle ABCDA as shown in the P-V diagram.  Column II give the characteristics involved in the cycle. Match them with each of the processes given in Column I. 

Question Image
                 Column I           Column II
A)Process  ABp)Internal energy decreases
B)Process  BCq)Internal energy increases
C)Process  CDr)Heat is lost
D)Process  DAs)Heat is gained
  t)Work is done on the gas

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a

A-prt; B-pr;  C-qs; D-rt

b

A-ps; B-rts; C-pqr; D-rst

c

A-pq; B-rs; C-rt; D-qrs

d

A-p; B-qr; C-rst; D-pqrs

answer is A.

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Detailed Solution

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A) Process  AB
This is an  isobaric process, P = constant and volume (V) 
of the gas decreases. Therefore work is done on the gas. 
 W=P(3VV)=2PV
Also V  decreases so temperature at B decreases 
 Internal energy U decreases. 
From,  Q=U+W as U and  W decreases so  Q decreases that means heat is lost. 
B) Process  BC
This is an isochoric process  V=constant pressure decreases 
PT  so temperature also decreases. 
W=0;   ΔU= negative so  ΔQ  negative 
Hence heat is lost. 
C) Process  CD
This is an isobaric, Pressure P=constant V increases and  VT  so T  increases. Hence ΔW, ΔU  and  ΔQ+ve so heat gained by the gas.
D) Process  DA
Applying  PV=nRT
For  D   P(9V)=1RTD    TD=9PVR
For  A  3P(3V)=1RTA        TA=9PVR
i.e., the process is isothermal              ΔU=0
now,  ΔQ=ΔU+W                             ΔQ=W.
As volume decreases in this process so  W negative i.e., 
Wom done on the gas and  ΔQ negative hence heat is lost. 

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