When the valve of the evacuated bottle is opened, atmospheric air rushes into it. If the atmospheric pressure is 101.325 kPa , and 0.6 m 3 of air (measured at atmospheric conditions) enters into the b

Question

When the valve of the evacuated bottle is opened, atmospheric air rushes into it. If the atmospheric pressure is 101.325 kPa , and 0.6 m 3 of air (measured at atmospheric conditions) enters into the bottle, calculate the work done (in kJ ) by air.

TestHub · Accepted Answer

The displacement work done by air W d ​ ​ = ∫ B o ttl e ​ p d V + ∫ F ree − ai r b o u n d a ry ​ ​ p d V = 0 + p Δ V = 101.325 k N / m 2 × 0.6 m 3 = 60.8 k J ​ Since the free-air boundary is contracting, the work done by the system is positive ( Δ V being negative), and the surroundings do positive work upon the system.

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