An ideal gas is compressed to half its initial volume by several possible processes. Which process results in the maximum work done ON the gas?
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Question

An ideal gas is compressed to half its initial volume by several possible processes. Which process results in the maximum work done ON the gas?

G1 Physics · Accepted Answer

Step 1: Compare compression from the SAME starting state to V₂ = V₁/2. Step 2: Under isobaric compression pressure remains P₁. Step 3: During an isothermal compression: P = P₁V₁/V. Step 4: During a reversible adiabatic compression: P = P₁(V₁/V)ᵞ, where γ > 1. Step 5: For V < V₁, the pressure ranking is: adiabatic > isothermal > isobaric. Step 6: The input work is the positive area under each P–V curve over that same volume interval. Therefore adiabatic compression needs the largest work input.…