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  4. A mixture of gases at NTP for which γ=1.5 is suddenly compressed to (1/9) th of its original volume. The final temperature of mixture is

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

Thermodynamics

Solution:

$T V^{\gamma-1}=$ constant
$T_{1}\, V_{1}^{\gamma-1}=T_{2} V_{2}^{\gamma-1}$
$T_{2}=T_{1}\left(\frac{V_{1}}{V_{2}}\right)^{\gamma-1}$
$T_{2}=(273\, K )\left[\frac{V_{1}}{V / 9}\right]^{1.5-1}$
$T_{2}=(273\, K ) \times 3$
$=819\, K$
$=546^{\circ} C$