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Equal amount of an ideal monoatomic gas at 400K is filled in two cylinders A and B. The piston A is free to move while that of  B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 45 K. Then the rise in temperature of gas in B

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\\\text{Since the piston of A is free to move, the pressure inside the cylinder A remains the same.} \\ \text{Thus, for given heat H to the system, } \\ $\mathrm{H}=\mathrm{n} \mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}_{1}$ \\\\ \text{The piston in cylinder B is fixed. Thus volume remains constant. } \\ $\mathrm{H}=\mathrm{n} \mathrm{C}_{\mathrm{V}} \Delta \mathrm{T}_{2}$

\begin{aligned} &\frac{C_{p}}{C_{v}}=\frac{\Delta T_{2}}{\Delta T_{1}}=\gamma\\ &\text { For a monoatomic gas is }\\ &\gamma=\frac{7}{5}\\ &\text { Hence } \mathrm{T}_{2}=\frac{7}{5} \times 45=63 \ \mathrm{K} \end{aligned}

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