Physics · The first law of thermodynamics, isothermal and adiabatic processes
A litre of dry air at STP expands adiabatically to a volume of 3 litres. If the
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: \( \left(3^{1.4}=4.6555\right) \) [Take air to be an ideal gas \( ] \)
- A. \( 48 \mathrm{J} \)
- B. \( 100.8 \mathrm{J} \)
- C. \( 60.7 J \)
- D. \( 90.5 J \)
Step-by-step solution
For an adiabatic process, work done by an ideal gas is W = (P1V1 - P2V2)/(γ-1). At STP: P1=1 atm, V1=1 L, so P1V1=1 atm·L = 101.325 J. For adiabatic expansion, P2 = P1(V1/V2)^γ = (1/3)^1.4 = 1/4.6555 ≈ 0.2148 atm, and V2=3 L, so P2V2 ≈ 0.6444 atm·L. Then W = (1 - 0.6444)/(0.4) = 0.889 atm·L = 0.889 × 101.325 ≈ 90.1 J, closest to 90.5 J.
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