Question

The volume of a gas is reduced adiabatically to ${\frac{1}{4}}^{th}$ of its orignal volume at ${27}^{\circ }$C. If $\gamma =1.4$, the new temperature of the gas will be

• A. $\left(300\right)2^{0.4}K$
  
• B. $\left(300\right)4^{1.4}K$
• C. $\left(300\right)4^{0.4}K$
• D. $\left(300\right)2^{1.4}K$
  

Answer 1

The correct option is C $\left(300\right)4^{0.4}K$

In adiabatic process,

$T{V}^{\gamma -1}$=constant
$T_2{V}_2^{\gamma -1}=T_1{V}_1^{\gamma -1}$
$T_2={\left(\frac{V_1}{V_2}\right)}^{\gamma -1}{T}_1$
$T_2={\left(4\right)}^{1.4-1}\left(300\right)=\left(300\right){\left(4\right)}^{0.4}K$