Question

An ideal gas at $27{}^{\circ }C$ is compressed adiabatically to $8/27$ of its original volume. If $\gamma =5/3$ , then the rise in temperature is

• A. $450K$
• B. $375K$
• C. $225K$
• D. $405K$

Answer 1

Answer: (B)

For an adiabatic process $T{V}^{\gamma -1}=\text{constant}$ ; where $T$ is temperature and $V$ denotes the volume, therefore,
$\frac{T_1}{T_2}={\left[\frac{V_2}{V_1}\right]}^{\gamma -1}$
$T_2=T_1{\left[\frac{V_1}{V_2}\right]}^{\gamma -1}$
$T_2=300{\left[\frac{27}{8}\right]}^{5/3-1}=300{\left[\frac{27}{8}\right]}^{2/3}=675K$
Hence, the change in temperature,
$\Delta T=675-300=375K$ .