Question

An insulated, vertical piston-cylinder assembly contains 50 L of steam at 105 oC. The outside pressure is 101 kPa. The piston has a diameter of 20 cm and the combined mass of the piston and the load is 75 kg. The electrical heater and the paddle wheel are turned on and the piston rises slowly by 25 cm with a constant pressure. The total internal energy increases by 3.109 kJ.

Determine:

a. The pressure of air inside the cylinder during the process.
b. The boundary work performed by the gas.
c. The combined work transfer by the shaft and electricity.

Answer 1

Step-by-step explanation:

From the given information:

The pressure of the air during the process =
`P_(atm) + P_(due \ to \ wt \ of \ piston)`

`= 101 \ kPa + (75 \ kg * 9.8 \ m/s^2 * (1 \ N )/(1 \ kg.m/s^2) )/((\pi)/(4)(0.2 \ m)^2) ( (1 \ N )/(m^2) * (1 \ kPa)/(1000 \ n/m^2))`

The pressure of the air during the process = 124.42 kPa

The boundary work = P × ΔW

The boundary work = 124.42 kPa × (π/4) × (0.2 m)² × 0.25 m × (1 kJ/1 kPa.m³)

The boundary work = 0.977 kJ

The combined work transfer =
`W_(boundary) + \Delta U`

The combined work transfer = 0.977 + 3.109 kJ

The combined work transfer = 4.086 kJ