Three moles of helium at 300 K occupy 30 litres. The gas is first expanded at constant pressure to three times its volume. Then it expands adiabatically until its temperature returns to 300 K. Find th

Question

Three moles of helium at 300 K occupy 30 litres. The gas is first expanded at constant pressure to three times its volume. Then it expands adiabatically until its temperature returns to 300 K. Find the total work done by the gas in kJ (one decimal).

TestHub · Accepted Answer

P 1 ​ = V n RT ​ = 249.4 kPa. Isobaric: T = 900 K, V = 90 litre, W 1 ​ = P Δ V = 14.97 kJ. Adiabatic from 900 K to 300 K: W 2 ​ = n C v ​ Δ T = 3 × 1.5 × 8.314 × 600 = 22.45 kJ. Total = 37.4 kJ. (Final volume 90 × 3 1.5 = 468 litre, final pressure 16.0 kPa.)

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