Three moles of an ideal gas are compressed isothermally from 60 L to 20 L using constant pressure of 5 atm. Heat exchange Q for the compression is - _________ Lit. atm.

Solution

Chemistry ma’am · 4 steps

Isothermal ideal gas means Δ U = 0, so the heat given out exactly equals the work done on it.

1. No energy change. The internal energy of an ideal gas depends only on temperature. The temperature stays fixed, so Δ U = 0 and the first law Δ U = Q + W gives Q = -W.
2. Irreversible work. The gas is pushed by a constant external pressure, so the work done on the gas is W = -PₑₓₜΔ V. Do not use the reversible nRT ln formula here.

   W = -Pₑₓₜ(V₂ - V₁) = -5 × (20 - 60) = +200 L atm

3. Find the heat. Q = -W = -200 L atm. The minus sign means the gas releases 200 L atm of heat to the surroundings.
4. So. The blank already carries the minus sign, so it is filled with 200.

The common slip: 600. Multiplying the work by the 3 moles gives 600. The term PₑₓₜΔ V already describes the whole gas, so n plays no part.

The idea to keep. For an ideal gas at constant temperature, Δ U = 0, so Q = -W. Against a constant external pressure, take W = -PₑₓₜΔ V. The number of moles does not enter.

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