A perfect gas is found to obey the relation P | vedclass

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(C) For an adiabatic process,the given relation is $PV^{3/2} = 	ext{constant}$.Using the ideal gas equation $PV = RT$,we can write $P = \frac{RT}{V}$

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$\sqrt{2}T$

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(C) For an adiabatic process,the given relation is $PV^{3/2} = 	ext{constant}$.Using the ideal gas equation $PV = RT$,we can write $P = \frac{RT}{V}$.Substituting this into the given relation: $\left(\frac{RT}{V}ight) V^{3/2} = 	ext{constant}$.This simplifies to $TV^{1/2} = 	ext{constant}$.Let the initial state be $(T_1, V_1)$ and the final state be $(T_2, V_2)$.Given $T_1 = T$ and $V_2 = \frac{V_1}{2}$.Using the relation $T_1 V_1^{1/2} = T_2 V_2^{1/2}$,we get:$T \cdot V_1^{1/2} = T_2 \cdot \left(\frac{V_1}{2}ight)^{1/2}$.$T = T_2 \cdot \frac{1}{\sqrt{2}}$.Therefore,$T_2 = \sqrt{2}T$.

$A$ perfect gas is found to obey the relation $PV^{3/2} =$ constant,during an adiabatic process. If such a gas,initially at a temperature $T$,is compressed adiabatically to half its initial volume,then its final temperature will be

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