- 2071 Magh
Gas under piston: pressure, volume doubled
Short answer
P = P_atm + W/A = 101000 + 490.5/0.01 = 150.05 kPa. Pressure does not change when volume doubles; piston equilibrium is set solely by external loads.
A cylinder encloses a gas with a piston as shown in Figure P.2. The area of piston is 0.01 m². Take the atmospheric pressure to be 0.101 MPa and the local gravitational acceleration as 9.81 m/s². If the weight of the piston is 490.50 N, what is the gas pressure? Will the gas pressure change if the gas volume beneath the piston is double? [Figure P.2: vertical cylinder of gas closed by a piston with a small weight/rod on top.]
Given: A = 0.01 m², P_atm = 0.101 MPa = 101 kPa, piston weight W = 490.5 N. (Only the piston weight is taken to act on the gas; the small rod/weight on top is neglected.)
Force balance on the piston (in equilibrium):
P·A = P_atm·A + W
P = P_atm + W/A
P = 101 000 + 490.5/0.01 = 101 000 + 49 050 = 150 050 Pa
Answer: Gas pressure = 150.05 kPa ≈ 0.15 MPa.
Does the pressure change if the gas volume is doubled?
No. The piston is free and in equilibrium, so the pressure is fixed only by the force balance: P = P_atm + W/A. This does not contain volume. If the gas volume doubles (for example by heating), the piston just moves up and the pressure remains 150.05 kPa (constant-pressure process), as long as the piston does not hit stops or a spring.
✓ Answer checked by Claude Opus 5.5 (high effort)
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