A monoatomic gas having gamma = 5/3 is stored | vedclass

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(C) Since the gas is in a thermally insulated container and is compressed suddenly,the process is adiabatic.For an adiabatic process,the relation betw

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$32$

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(C) Since the gas is in a thermally insulated container and is compressed suddenly,the process is adiabatic.For an adiabatic process,the relation between pressure $P$ and volume $V$ is given by $P_i V_i^\gamma = P_f V_f^\gamma$.Here,$V_f = \frac{1}{8} V_i$,which implies $\frac{V_i}{V_f} = 8$.The ratio of final pressure to initial pressure is $\frac{P_f}{P_i} = \left(\frac{V_i}{V_f}\right)^\gamma$.Substituting the values,$\frac{P_f}{P_i} = (8)^{5/3}$.Since $8 = 2^3$,we have $(2^3)^{5/3} = 2^5 = 32$.Thus,the ratio of final pressure to initial pressure is $32$.

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