An ideal gas is found to obey Pv^{frac{3}{2}} | vedclass

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(C) Given the adiabatic process equation: $Pv^{\frac{3}{2}} = 	ext{constant}$ ... $(i)$From the ideal gas law: $PV = nRT$,we have $P = \frac{nRT}{V}$

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$2 T$

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(C) Given the adiabatic process equation: $Pv^{\frac{3}{2}} = 	ext{constant}$ ... $(i)$From the ideal gas law: $PV = nRT$,we have $P = \frac{nRT}{V}$ ... (ii)Substituting (ii) into $(i)$:$\left(\frac{nRT}{V}ight) V^{\frac{3}{2}} = 	ext{constant}$$T V^{\frac{1}{2}} = 	ext{constant}$Therefore,$T_1 V_1^{\frac{1}{2}} = T_2 V_2^{\frac{1}{2}}$Given initial temperature $T_1 = T$ and final volume $V_2 = \frac{V_1}{4}$:$T V_1^{\frac{1}{2}} = T_2 \left(\frac{V_1}{4}ight)^{\frac{1}{2}}$$T = T_2 \left(\frac{1}{4}ight)^{\frac{1}{2}}$$T = T_2 \left(\frac{1}{2}ight)$$T_2 = 2T$

An ideal gas is found to obey $Pv^{\frac{3}{2}} = \text{constant}$ during an adiabatic process. If such a gas initially at a temperature $T$ is adiabatically compressed to $\frac{1}{4}$th of its volume,then its final temperature is

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