Question

A cyclic process (cycle) 1 - 2 - 3 - 4 - 1 consisting of two isobars 2 - 3 and 4 - 1, isochor 1- 2, and a certain process 3 - 4 represented by a straight line on the p-V diagram (Fig. 57) involves n moles of an ideal gas. The gas temperatures in states 1, 2, and 3 are T₁, T₂, and T₃ respectively, and points 2 and 4 lie on the same isotherm. 

Determine the work A done by the gas during the cycle.

Answer 1

The work A done by the gas during the cycles determined by the area of the p-V diagram bounded by the cycle, i.e. by the area of the trapezoid (see Fig. 57):

All these quantities can easily be expressed in terms of pressure and volume p₁ and V₁ at point 1. Indeed, according to Charles's law, V₃ = V₂T₃/ T₂ = V₁T₃/ T₂ and V₄ = V₁T₄/ T₁ = V₁T₂/T₁, while the Gay-Lussac law implies that p₂ = p₁T₂/T₁. Substituting these values into the expression for work, we obtain

The equation of state for n moles of an ideal gas is p₁V₁ = nR T₁, and we can finally write