If a gas of volume 400 cc at an initial pres | vedclass

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(B) sudden compression of a gas is an adiabatic process.For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $P_1 V_1

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$8P$

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(B) sudden compression of a gas is an adiabatic process.For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $P_1 V_1^\gamma = P_2 V_2^\gamma$,where $\gamma$ is the adiabatic index (ratio of specific heat capacities).Given:Initial pressure $P_1 = P$Initial volume $V_1 = 400 \ cc$Final volume $V_2 = 100 \ cc$Adiabatic index $\gamma = 1.5 = 3/2$Substituting the values into the adiabatic equation:$P 	imes (400)^{3/2} = P_2 	imes (100)^{3/2}$$P_2 = P 	imes (400/100)^{3/2}$$P_2 = P 	imes (4)^{3/2}$$P_2 = P 	imes (2^2)^{3/2}$$P_2 = P 	imes 2^3$$P_2 = 8P$Therefore,the final pressure is $8P$.

If a gas of volume $400 \ cc$ at an initial pressure $P$ is suddenly compressed to $100 \ cc$,then its final pressure is (The ratio of the specific heat capacities of the gas at constant pressure and constant volume is $1.5$).

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