Question

An ideal gas at ${27}^{\circ }\text{C}$ is compressed adiabatically to $\frac{4}{9}$ of its original volume. If $\gamma =1.5$, then the final temperature of the gas is

• A. $300\text{K}$
• B. $400\text{K}$
• C. $450\text{K}$
• D. $200\text{K}$

Answer 1

The correct option is C $450\text{K}$

Given,
Initial temperature $\left(T_1\right)=300\text{K}$
Initial volume $\left(V_1\right)=V$
Final volume $\left(V_2\right)=\frac{4}{9}V$
Final temperature $\left(T_2\right)=?$
Adiabatic index $\left(\gamma \right)=1.5$
For an adiabatic change,
$T_1{V}_1^{\gamma -1}=T_2{V}_2^{\gamma -1}$
$\Rightarrow T_2=T_1{\left(\frac{V_1}{V_2}\right)}^{\gamma -1}=\frac{3}{2}{T}_1$
$=450\text{K}$