The pressure $\mathrm{P}_{1}$ and density $\mathrm{d}_{1}$ of diatomic gas $\left(\gamma=\frac{7}{5}\right)$ changes suddenly to $\mathrm{P}_{2}\left(>\mathrm{P}_{1}\right)$ and $\mathrm{d}_{2}$ respectively during an adiabatic process. The temperature of the gas increases and becomes ________ times of its initial temperature. (given $\frac{\mathrm{d}_{2}}{\mathrm{~d}_{1}}=32$)
Answer (integer)
4
Solution
<p>${P_1}V_1^\gamma = {P_2}V_2^2$</p>
<p>${{{P_1}} \over {d_1^\gamma }} = {{{P_2}} \over {d_2^\gamma }}$</p>
<p>${{{d_1}{T_1}} \over {d_1^\gamma }} = {{{d_2}{T_2}} \over {d_2^\gamma }}$</p>
<p>${T_2} = {\left( {{{{d_2}} \over {{d_1}}}} \right)^{\gamma - 1}}{T_1}$</p>
<p>$= {(32)^{{2 \over 5}}}{T_1}$</p>
<p>${T_2} = 4\,{T_1}$</p>
About this question
Subject: Physics · Chapter: Thermodynamics · Topic: Zeroth and First Law
This question is part of PrepWiser's free JEE Main question bank. 271 more solved questions on Thermodynamics are available — start with the harder ones if your accuracy is >70%.