An ideal gas undergoes four different processes from the same initial state as shown in the P–V diagram. The processes are adiabatic, isothermal, isobaric and isochoric. Curve 1 is vertical, curve 4 is horizontal, and curves 2 and 3 fall as V increases. Which curve represents the adiabatic process?
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Question

An ideal gas undergoes four different processes from the same initial state as shown in the P–V diagram. The processes are adiabatic, isothermal, isobaric and isochoric. Curve 1 is vertical, curve 4 is horizontal, and curves 2 and 3 fall as V increases. Which curve represents the adiabatic process?

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G1 Physics · Accepted Answer

Step 1: A vertical line on a P–V diagram represents V = constant. Therefore process 1 is isochoric. Step 2: A horizontal line represents P = constant. Therefore process 4 is isobaric. Step 3: At the SAME point, the magnitude of the isothermal slope is |dP/dV| = P/V because PV = constant. Step 4: For an adiabatic ideal gas, PVᵞ = constant, so |dP/dV| = γP/V, which is larger because γ > 1. Step 5: In the given graph, curve 2 falls more steeply than curve 3; therefore curve 2 is adiabatic. Final a…