Suppose that an ideal gas at 300 K and 200 kPa (abs.) is enclosed in a cylinder

Question

Suppose that an ideal gas at 300 K and 200 kPa (abs.) is enclosed in a cylinder by a frictionless (ideal) piston, and the gas slowly forces the piston so that the volume of gas expands from 0.1 to 0.2 m3. Two different paths are used to go from the initial state to the final state: Path A: The expansion occurs at constant pressure (isobaric), P = 200 kPa. Path B: The expansion occurs at constant temperature (isothermal), T = 300 K.

(a) On a P-V diagram, sketch the 2 paths from the initials state to the final state, and use the graph to determine which path involved more work done by the expanding gas.

(b) Confirm your answer in (a) by calculating the work done by the gas on the piston for each path.  

Explanation / Answer

• Path 1: expansion occurs at constant pressure (p = 200 kPa)
• Path 2: expansion occurs at constant temperature (T = 300 K)

W=p dV = p (V2 V1)
= 5.00 × 105 kPa (0.2m3 0.1m3) = 50kJ

Remember 1 J = 1 N·m.
Path 2,w=nRT ln(V2/V1)
(5.0 × 105Pa)(0.1m3)
(300K)(8.314 Pam3/mol K)
= 20.0 mol (5)
W = (20.0mol)(8.314 Pam3/mol K)(300K) ln(0.2/0.1) = 34.57kJ

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