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

Question

A mixture of gases at NTP for which &gamma;=1.5 is suddenly compressed to (1/9) th of its original volume. The final temperature of mixture is (A) 300° C (B) 546° C (C) 420° C (D) 872° C

Tardigrade Admin · Accepted Answer

T V&gamma;-1= constant T1 V1&gamma;-1=T2 V2&gamma;-1 T2=T1((V1/V2))&gamma;-1 T2=(273 K )[(V1/V / 9)]1.5-1 T2=(273 K ) × 3 =819 K =546° C

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

$30 0^{\circ} C$

$54 6^{\circ} C$

$42 0^{\circ} C$

$87 2^{\circ} C$

$T V^{γ - 1} =$ constant
$T_{1} V_{1}^{γ - 1} = T_{2} V_{2}^{γ - 1}$
$T_{2} = T_{1} (\frac{V _{1}}{V _{2}})^{γ - 1}$
$T_{2} = (273 K) [\frac{V _{1}}{V /9}]^{1.5 - 1}$
$T_{2} = (273 K) \times 3$
$= 819 K$
$= 54 6^{\circ} C$

Q. A mixture of gases at NTP for which γ=1.5 is suddenly compressed to 91​ th of its original volume. The final temperature of mixture is

300∘C

546∘C

420∘C

872∘C