A mixture of gases at STP for which gamma=1.5 is suddenly compressed to frac{1}{9} th of its origina

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11.Thermodynamics

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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 mixture is .......... $^{\circ} C$

A

$300$

B

$546$

C

$420$

D

$872$

Solution

(b)

$T V^{1-1}=\text { constant }$

$T_1 V_1^{\gamma-1}=T_2 V_2^{\gamma-1}$

$T_2=T_1\left(\frac{V_1}{V_2}\right)^{\gamma-1}$

$T_2=(273 \,K )\left[\frac{V_1}{V / 9}\right]^{1.5-1}$

$T_2=(273 \,K ) \times 3$

$=819 \,K$

$=546^{\circ} C$

Standard 11

Physics

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