A gas at N.T.P. is suddenly compressed to one | vedclass

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(C) Since the compression is sudden,the process is adiabatic.For an adiabatic process,the relation between pressure and volume is given by $P_1 V_1^\g

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(C) Since the compression is sudden,the process is adiabatic.For an adiabatic process,the relation between pressure and volume is given by $P_1 V_1^\gamma = P_2 V_2^\gamma$.Given: $V_2 = \frac{V_1}{4}$,so $\frac{V_1}{V_2} = 4$.Given: $\gamma = 1.5 = \frac{3}{2}$.Substituting these values into the equation:$\frac{P_2}{P_1} = \left( \frac{V_1}{V_2} \right)^\gamma = (4)^{3/2}$.Calculating the value: $(4)^{3/2} = (2^2)^{3/2} = 2^3 = 8$.Therefore,the final pressure $P_2 = 8 P_1$,which is $8$ times the initial pressure.

$A$ gas at $N.T.P.$ is suddenly compressed to one-fourth of its original volume. If $\gamma = 1.5$,then the final pressure is

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