A rigid steel tank initially contains an ideal gas at state
PHYSICS · Multi-part · A Level · Physics · Further mechanics and thermal physics · Further mechanics and thermal physics
Problem
A rigid steel tank initially contains an ideal gas at state (P0,V0,T0). A valve connects the tank to a long, narrow cylinder fitted with a light, frictionless piston. The cylinder is immersed in an ice–water mixture that maintains the gas inside the cylinder at a constant temperature T0.
The valve is opened, allowing gas to flow from the tank into the cylinder until the pressure inside the cylinder reaches 21P0, at which point the valve is closed. Assume the amount of gas that leaves the tank is small enough that the temperature of the gas remaining in the tank does not change appreciably from T0 during this transfer.
(a) Derive an expression for the volume Vc of the gas now inside the cylinder in terms of the initial tank volume V0.
(b) After the valve is closed, the gas inside the cylinder is slowly heated at constant pressure (21P0) until its temperature reaches 2T0. Determine the new volume Vd of the gas in the cylinder in terms of Vc.
(c) Using your results from parts (a) and (b), express Vd solely in terms of the initial tank volume V0.
(d) Discuss briefly whether the ideal-gas assumption is essential to the proportional relationships you obtained in parts (a)–(c).