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]

Solution

Physics sir · 4 steps

Use the adiabatic work formula. Get the final pressure from PV^γ being constant, then subtract.

1. Adiabatic work. For an adiabatic process the work done by the gas is the drop in PV divided by γ - 1.

   W = (P₁V₁ - P₂V₂)/(γ - 1)

2. Final state. From P₁V₁^γ = P₂V₂^γ we get P₂ = P₁(V₁/V₂)^γ = P₁/3^(1.4). So P₂V₂ = P₁V₁ × 3/4.6555 = 0.6444 P₁V₁.
3. Put in numbers. At STP, P₁V₁ = 1.013 × 10⁵ Pa × 10⁻³ m³ = 101.3 J. Then W = (101.3 × (1 - 0.6444))/0.4 = 36.02/0.4 ≈ 90.1 J.
4. So. The work done by the air is about 90 J. Option (c), 90.5 J, is the closest. The small gap comes from rounding 3^(1.4) and the value taken for 1 atm.

The idea to keep. For adiabatic work, find the final pressure from PV^γ = constant, then use W = (P₁V₁ - P₂V₂)/(γ - 1). With 1 litre at 1 atm, PV is about 101.3 J.

Answer from the NTA final answer key. Solution by PrepWiser.