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n moles of an ideal gas undergo the process A→ B shown in the figure. The maximum temperature of the gas during the process will be

Asked in JEE Main 2016 · Work from a Stated P-V Law

Figure: Work from a Stated P-V Law
Answer: (1) (9P₀V₀)/(4nR)

Step-by-step solution

The process A to B is the straight line in the figure, running from

A(V₀,2P₀) down to B(2V₀,P₀), so P=3P₀-(P₀)/(V₀)V.

T=(PV)/(nR)=1/(nR)(3P₀V-(P₀)/(V₀)V²).

(dT)/(dV)=0 gives 3P₀=(2P₀)/(V₀)V, so V=3/2V₀.

Tₘₐₓ=1/(nR)((9P₀V₀)/2-(9P₀V₀)/4)=(9P₀V₀)/(4nR).

Why the other options are wrong

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