A monoatomic gas (gamma = 5/3) initially at 2 | vedclass

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(C) Since the compression is sudden,it is an adiabatic process.For an adiabatic process,the relationship between temperature and volume is given by $T

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$1200$

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(C) Since the compression is sudden,it is an adiabatic process.For an adiabatic process,the relationship between temperature and volume is given by $T_1 V_1^{\gamma-1} = T_2 V_2^{\gamma-1}$.Given: $T_1 = 27^{\circ} C = 27 + 273 = 300 \ K$,$V_1 = V$,$V_2 = V/8$,and $\gamma = 5/3$.Substituting the values:$T_2 = T_1 \left( \frac{V_1}{V_2} ight)^{\gamma-1}$$T_2 = 300 	imes \left( \frac{V}{V/8} ight)^{(5/3) - 1}$$T_2 = 300 	imes (8)^{2/3}$$T_2 = 300 	imes (2^3)^{2/3} = 300 	imes 2^2 = 300 	imes 4 = 1200 \ K$.

$A$ monoatomic gas $(\gamma = 5/3)$ initially at $27^{\circ} C$ having volume $V$ is suddenly compressed to one-eighth of its original volume $(V/8)$. What is the final temperature after the compression (in $K$)?

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