Q.

One mole of a monoatomic ideal gas goes through a thermodynamic cycle, as shown in the volume versus temperature (V-T) diagram. The correct statement(s) is/are:
[R is the gas constant]
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a

The ratio of heat transfer during processes  12  and  23  is  |Q12Q23|=53

b

The ratio of heat transfer during processes 12  and  34 is    |Q12Q34|=12

c

Work done in this thermodynamic cycle  (12341)  is  |W|=12RT0

d

The above thermodynamic cycle exhibits only isochoric and adiabatic processes.   

answer is A, C.

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Detailed Solution

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A)  W=W12+W23+W34+W41=R(T2T1)+0+R(T4T3)+0    =R(2T0T0)+R(T02T0)=RT0RT02       W=RT02

C)  Q12=nCp(T2T1)=1×5R2(2T0T0)=52RT0           Q23=nCvΔT=1×3R2(T3T2)=3R2(T02T0)=32RT0            |Q12||Q23|=53           Q34=nCp(T4T3)=1×5R2(T02T0)=5R2T02=54RT0           |Q12||Q34|=5/25/4=2

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