A frictionless, moveable piston of cross-sectional area 0.025m2 confines an ideal gas within a vertical cylinder. The upper surface of the piston supports a column of oil of height 0.60m and density 800kgm−3. The top of the oil column is open to the atmosphere at standard atmospheric pressure 1.01×105Pa. A laboratory mechanism can apply an additional downward force Fappl on the piston to keep it stationary when the gas pressure increases during slow heating.
(a) Calculate the total external pressure acting on the top surface of the piston due to the atmosphere and the oil column alone, before any additional force is applied.
(b) Determine the gauge pressure the confined gas must reach so that the piston remains in equilibrium without any applied force Fappl.
(c) Derive an expression for the magnitude of the additional downward force Fappl that must be applied to keep the piston stationary when the gas pressure rises to a higher value Pg (gauge), where Pg exceeds the value found in part (b). Your expression may include Pg, numerical constants, and given quantities.
(d) Using your expression from part (c), calculate Fappl when the gauge pressure of the gas is 1.60×105Pa.