Question

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:

• A. 300${}^0$ C
• B. 546${}^0$ C
• C. 420${}^0$ C
• D. 872${}^0$ C

Answer 1

The correct option is B 546${}^0$ C

$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$

Given that

$V_2=V_1\frac{1}{9}$

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

$=T_1(9{)}^{0.5}$

$=3\times 273K$

$=819K={546}^o$C