A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:
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A gas is compressed isothermally to half of its initial volume. The same gas is compressed separately through an adiabatic process until its volume is again reduced to half. Then:

G1 Physics · Accepted Answer

Step 1: Both processes start at the same P₁, V₁ and finish at volume V₂ = V₁/2. Step 2: Isothermal compression follows PV = constant. At any intermediate volume V: P = P₁V₁/V. Step 3: Reversible adiabatic compression follows PVᵞ = constant. At volume V: P = P₁(V₁/V)ᵞ. Step 4: During compression V < V₁; since γ > 1, the adiabatic pressure is larger than the isothermal pressure at the SAME V. Step 5: Work input (magnitude) equals the area under the P–V curve between V₂ and V₁, i.e. ∫P dV with the…