JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Heat & Thermodynamics

A certain amount of gas of volume V at

2 7^{\circ} C

temperature and pressure

2 \times 1 0^{7} Nm^{- 2}

expands isothermally until its volume gets doubled. Later it expands adiabatically until its volume gets redoubled. The final pressure of the gas will be (Use

γ = 1.5

)

(A) $3.536 \times 1 0^{5} Pa$
(B) $3.536 \times 1 0^{6} Pa$ ✓ Correct
(C) $1.25 \times 1 0^{6} Pa$
(D) $1.25 \times 1 0^{5} Pa$

Answer: (B)

Solution

Isothermal expansion (

V_{1} \to V_{2} = 2 V_{1}

P_{1} V_{1} = P_{2} V_{2} \Rightarrow P_{2} = \frac{P _{1}}{2} = \frac{2 \times 1 0 ^{7}}{2} = 1 \times 1 0^{7} Pa

Adiabatic expansion (

V_{2} \to V_{3} = 2 V_{2}

P_{2} V_{2}^{γ} = P_{3} V_{3}^{γ} \Rightarrow P_{3} = P_{2} (\frac{V _{2}}{V _{3}})^{γ} = P_{2} (\frac{1}{2})^{1.5}

P_{3} = \frac{1 \times 1 0 ^{7}}{2 ^{1.5}} = \frac{1 \times 1 0 ^{7}}{2 2} \approx \frac{1 \times 1 0 ^{7}}{2.828} \approx 3.536 \times 1 0^{6} Pa

JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Single correct option

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JEE Main · 2022 · 25 Jul 2022 · Shift 1 · Heat & Thermodynamics

Solution

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