Question

A monatomic ideal gas initially at ${17}^{o}C$ is suddenly compressed to $\frac{1}{8}$ of its original volume. The temperature after compression is

• A. ${17}^{o}C$
• B. ${136}^{o}C$
• C. ${887}^{o}C$
• D. ${240}^{o}C$

Answer 1

The correct option is C ${887}^{o}C$

Suddenly compressed implies no time for heat exchange with the surroundings. So, can be treated as an adiabatic process.

Relationship between volume and temperature is
$T{V}^{\gamma -1}=$constant
$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
$290(V{)}^{\frac{5}{3}-1}=T_2{\left(\frac{V}{8}\right)}^{\frac{5}{3}-1}$
$T_2=290{\left(\frac{V}{V/8}\right)}^{2/3}=290(8{)}^{2/3}=1160K={887}^{o}C$