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JEE Main 2022 (29 Jul, Shift 1) · Thermodynamic Processes

Thermodynamic Processes question from JEE Main 2022 (29 Jul, Shift 1)

Q168JEE Main 2022 · 29 JUL · SHIFT 1Medium

Thermodynamic Processes

The pressure $P_1$ and density $d_1$ of diatomic gas $\left(\gamma = \frac{7}{5}\right)$ changes suddenly to $P_2\ (> P_1)$ and $d_2$ respectively during an adiabatic process. The temperature of the gas increases and becomes ________ times of its initial temperature. (given $\frac{d_2}{d_1} = 32$ )

Numerical answer type. Work it out, then open the answer.

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Answer: 4

$TV^{\gamma-1} =$ const and $\rho \propto \frac{1}{V}$ , so $T \propto \rho^{\gamma-1}$ .
$\frac{T_2}{T_1} = 32^{2/5} = (2^5)^{2/5} = 2^2$
$\frac{T_2}{T_1} = 4$

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