A mixture of gases at STP for which gamma = 1 | vedclass

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(B) For an adiabatic process,the relation between temperature and volume is given by $T V^{\gamma-1} = 	ext{constant}$.Given:Initial temperature $T_1

Vedclass · Accepted Answer

$546$

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(B) For an adiabatic process,the relation between temperature and volume is given by $T V^{\gamma-1} = 	ext{constant}$.Given:Initial temperature $T_1 = 273 \, K$ (at $STP$).Initial volume $V_1 = V$.Final volume $V_2 = \frac{V}{9}$.Adiabatic index $\gamma = 1.5$.Using the relation $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$:$T_2 = T_1 \left( \frac{V_1}{V_2} ight)^{\gamma-1}$$T_2 = 273 	imes \left( \frac{V}{V/9} ight)^{1.5-1}$$T_2 = 273 	imes (9)^{0.5}$$T_2 = 273 	imes 3 = 819 \, K$.To convert the temperature to Celsius:$T(^{\circ}C) = T(K) - 273$$T(^{\circ}C) = 819 - 273 = 546 \, ^{\circ}C$.

$A$ mixture of gases at $STP$ for which $\gamma = 1.5$ is suddenly compressed to $\frac{1}{9}$th of its original volume. The final temperature of the mixture is .......... $^{\circ}C$.

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