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Q.

As shown in the above graph, a monoatomic ideal gas whose initial temperature is T0 at the point A is taken to the final state at point C via point B. Now, choose the correct statement:

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a

Work done by the gas is RT0

b

Change in internal energy of the gas is 112RT0

c

Heat absorbed by the gas is 92RT0

d

Heat absorbed by the gas is 132RT0

answer is A.

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Detailed Solution

Work done = Area of ABC with respect to volume axis i.e V-axis= area under AB = area under BC=P02V0−V0+0=P0V0=nRT0=RT0(∵n=1, one mole given )where R is gas constant.Change in internal energy=ΔU=nCνΔT where Cv is specific heat capacity at constant volume and is equal to 32R for monoatomic gas=1×32R×4T0−T0=92RT0(at C, Temperature T = 4T0 due to 2Po×2Vo=nRT and PoVo = nR0)∴ Heat absorbed=ΔU+ΔW=92RT0+RT0=112RT0Hence, only option 1 is correct.
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As shown in the above graph, a monoatomic ideal gas whose initial temperature is T0 at the point A is taken to the final state at point C via point B. Now, choose the correct statement: