An ideal gas undergoes a clockwise cyclic process consisting of three steps. The states of the gas at the vertices of the cycle on a P-V diagram are (V₀, 2P₀) , (3V₀, 2P₀) , and (V₀, P₀) . What is the ratio of the work done by the gas during the isobaric expansion segment to the net work done by the gas in the entire cycle?

Step-by-step solution

The cyclic process forms a right-angled triangle on the P-V diagram. The isobaric expansion occurs at a constant pressure of 2P₀ from volume V₀ to 3V₀ . Work done during this expansion, W_ exp = P V = 2P₀(3V₀ - V₀) = 4P₀V₀ . The net work done in the clockwise cycle is the area of the triangle enclosed on the P-V diagram. Base of the triangle (change in volume) = 3V₀ - V₀ = 2V₀ . Height of the triangle (change in pressure) = 2P₀ - P₀ = P₀ . Net work, W_ net = 1 2 base height = 1 2 2V₀ P₀ = P₀V₀ . The required ratio