One mole of ideal gas passes through a process where pressure and… | JEE Main 2019 (10 Apr, Shift 2)

Q218JEE Main 2019 · 10 APR · SHIFT 2Difficult

Thermodynamic Processes

One mole of ideal gas passes through a process where pressure and volume obey the relation ${}$

$P = P_0\left[1 - \frac{1}{2}\left(\frac{V_0}{V}\right)^{2}\right]$ . Here P0 and V0 are constants. Calculate the change in the temperature of the gas if its volume changes form V0 to 2V0

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Answer: (c)

One mole: $T = \frac{PV}{R}$ .
At $V_0$ : $P = \frac{P_0}{2}$ , so $T_1 = \frac{P_0V_0}{2R}$ .
At $2V_0$ : $P = P_0\left(1 - \frac{1}{8}\right) = \frac{7P_0}{8}$ , so $T_2 = \frac{7P_0V_0}{4R}$ .
$\Delta T = \frac{7}{4} - \frac{2}{4} = \frac{5}{4}\frac{P_0V_0}{R}$ , so the answer is (c).

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