A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm

Question

A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm from a volume of 5 litres to a volume of 10 litres. In doing so it absorbs 400 J of thermal energy from its surroundings. Determine the change in internal energy of system.

Anonymous · Accepted Answer

Answer: Δ U = -106.5\ J (internal energy decreases by 106.5 J) Given: P = 1\ atm = 1.013×10⁵\ Pa, V₁ = 5\ L, V₂ = 10\ L, heat absorbed Q = +400\ J Δ V = 10 - 5 = 5\ L = 5×10⁻³\ m³ Work done by the gas against the constant external pressure: W = PΔ V = 1.013×10⁵×5×10⁻³ = 506.5\ J First law of thermodynamics: Q = Δ U + W Δ U = Q - W = 400 - 506.5 = -106.5\ J The gas does 506.5 J of work but receives only 400 J of heat, so the remaining 106.5 J comes from its internal energy. Hence internal energy decreases by 106.5 J.

Doubtly AI · Answer

Answer: Δ U = -106.5 J (the internal energy decreases by 106.5 J) Work done by the gas against constant external pressure: P = 1\ atm = 1.013×10⁵ Pa Δ V = 10 - 5 = 5\ L = 5×10⁻³\ m³ W = PΔ V = 1.013×10⁵×5×10⁻³ = 506.5\ J W is positive because the gas expands (work done by the system). First law of thermodynamics: Q = Δ U + W, with Q = +400 J (heat absorbed). Δ U = Q - W = 400 - 506.5 = -106.5\ J The gas does more work than the heat it absorbs, so it uses some of its own internal energy: its internal energy falls by 106.5 J.

A gas contained in a cylinder fitted with a frictionless piston expands against a constant external pressure of 1 atm

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