One mole of an ideal gas passes through a process where pressure and volume obey the relation $P=P_{o}\left[1-\frac{1}{2}\left(\frac{V_{o}}{V}\right)^{2}\right]$. Here $P_{o}$ and $V_{o}$ are constants. Calculate the change in the temperature of the gas if its volume change from $V_{o}$ to $2V_{o}$

(C) $\frac{5}{4} \frac{P_{o} V_{o}}{R}$

(A) $\frac{1}{4} \frac{P_{o} V_{o}}{R}$

(B) $\frac{1}{2} \frac{P_{o} V_{o}}{R}$

(D) $\frac{3}{4} \frac{P_{o} V_{o}}{R}$

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Heat & Thermodynamics

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

P = P_{o} [1 - \frac{1}{2} (\frac{V _{o}}{V})^{2}]

. Here

P_{o}

and

V_{o}

are constants. Calculate the change in the temperature of the gas if its volume change from

V_{o}

2 V_{o}

Answer: (C)

For one mole

T = \frac{P V}{R}

. At

V = V_{0}

P = P_{0} (1 - \frac{1}{2}) = \frac{P _{0}}{2}

T_{1} = \frac{P _{0} V _{0}}{2 R}

; at

V = 2 V_{0}

P = P_{0} (1 - \frac{1}{2} \cdot \frac{1}{4}) = \frac{7 P _{0}}{8}

T_{2} = \frac{7 P _{0}}{8} \cdot \frac{2 V _{0}}{R} = \frac{7 P _{0} V _{0}}{4 R}

. The change is

Δ T = \frac{7 P _{0} V _{0}}{4 R} - \frac{P _{0} V _{0}}{2 R} = \frac{5 P _{0} V _{0}}{4 R}

JEE Main · 2019 · 10 Apr 2019 · Shift 2 · Single correct option