A gas has an internal energy given by the relation U = 1.5 pV . The gas expands from 100 cm ^3 to 200 cm ^3 against a constant pressure of 1.0 10^5 Pa . Determine the heat absorbed by the gas during this process.

Step-by-step solution

The process is isobaric, so the pressure p of the gas is constant and equal to the external pressure. The work done by the gas during the expansion is given by W = p V = p(V₂ - V₁) . Substituting the given values: W = 1.0 10^5 (200 - 100) 10⁻⁶ = 1.0 10^5 10⁻⁴ = 10 J The change in internal energy is U = U₂ - U₁ = 1.5 p₂ V₂ - 1.5 p₁ V₁ . Since the pressure is constant, p₁ = p₂ = p , giving U = 1.5 p(V₂ - V₁) = 1.5 W . U = 1.5 10 = 15 J According to the first law of thermodynamics, the heat absorbed by the gas is Q =