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

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(C) For an adiabatic compression,the relation is $PV^{\gamma} = 	ext{constant}$.Given: $V_{	ext{new}} = \frac{1}{4} V$ and $\gamma = \frac{3}{2}$.Us

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$8\ P$

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(C) For an adiabatic compression,the relation is $PV^{\gamma} = 	ext{constant}$.Given: $V_{	ext{new}} = \frac{1}{4} V$ and $\gamma = \frac{3}{2}$.Using the adiabatic process equation:$P_1 V_1^{\gamma} = P_2 V_2^{\gamma}$$P \cdot V^{\gamma} = P_{	ext{new}} \cdot \left(\frac{V}{4}ight)^{\gamma}$$\frac{P_{	ext{new}}}{P} = \left(\frac{V}{V/4}ight)^{\gamma} = (4)^{\gamma}$$\frac{P_{	ext{new}}}{P} = (4)^{3/2} = (2^2)^{3/2} = 2^3 = 8$Therefore,$P_{	ext{new}} = 8P$.

$A$ gas at $N.T.P.$ is suddenly compressed to $\left(\frac{1}{4}\right)$ of its original volume. What will be the final pressure? (Given: $\gamma = \text{ratio of specific heats} = \frac{3}{2}$,$P = \text{original pressure}$)

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