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Two samples A and B of a gas initially at the same pressure and temperature are compressed from volume $V$ to $V / 2 .$ ( A isothermally and B adiabatically).The final pressure of A is

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greater than the final pressure of B

equal to the final pressure of B

less than the final pressure of B

twice the final pressure of B

answer is C.

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Detailed Solution

For isothermal process, $P_{1} V = P_{2}^{'} \frac{V}{2} \Rightarrow P_{2}^{'} = 2 P_{1} . . . . . . . . . (i)$

For adiabatic process, $P_{1} V^{γ} = P_{2} {(\frac{V}{2})}^{γ} \Rightarrow P_{2} = 2^{γ} P_{1} . . . . . . . . . . (i i)$

Since $γ > 1, P_{2} > P_{2}^{'}$

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