A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $\gamma = 1.40$, the work done by air is: ($3^{1.4} = 4.6555$) [Take air to be an ideal gas]

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Heat & Thermodynamics

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If

γ = 1.40

, the work done by air is: (

3^{1.4} = 4.6555

) [Take air to be an ideal gas]

(A)48 J
(B)90.5 J✓ Correct
(C)100.8 J
(D)60.7 J

Answer: (B)

Solution

For the adiabatic expansion the work done by the gas is

W = \frac{P _{1} V _{1} - P _{2} V _{2}}{γ - 1}

, with

P_{2} = P_{1} (\frac{V _{1}}{V _{2}})^{γ} = \frac{P _{1}}{3 ^{1.4}} = \frac{P _{1}}{4.6555}

. Taking

P_{1} = 1.01 \times 1 0^{5} Pa

V_{1} = 1 0^{- 3} m^{3}

and

V_{2} = 3 \times 1 0^{- 3} m^{3}

gives

P_{1} V_{1} \approx 101.3 J

and

P_{2} V_{2} \approx 65.3 J

, so

W \approx \frac{101.3 - 65.3}{0.4} \approx 90 J

JEE Main · 2020 · 07 Jan 2020 · Shift 1 · Single correct option

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