Question

A vertical piston cylinder arrangement consists of a spring and two stops as shown in
following Fig. Piston diameter is 20 cm, and mass is 10 kg. Piston is frictionless and is free to move between the stops (H1=10 cm and H2=20cm). Assume the thickness of piston and stops to be negligible. Spring is linear, with K=20 kN/m and natural length=15 cm. Initially, the piston is held at the upper stop. It contains air at a pressure 200 kPa and 800K. Heat is gradually extracted from the system till the pressure reaches 50 kPa and the piston is situated on the lower stop. Make suitable assumptions and take data for standards constants
(a) Find the net work done by the system
(b) Find total heat extracted from the system. Assume specific heat to be 0.9 kJ/kg K
(c) Draw the complete process on a P-V diagram. Show all pressure and volume values

Answer 1

Answer:

When pressure changes from 1 atm to 3 atm, the change in pressure

P=2atm

=2×1×105N/m2

The force exerted on the piston

F=PA=2×105×4×10−4

=80N

The compression of the spring

x=kF=10480=0.008m

The change in volume of air due to displacement of piston by x

ΔV=Ax=4×10−4×0.008

=3.2×10−6m3

∴ Final volume, V2=V1+ΔV

=20×10−6+3.2×10−6

By equation of state

T1P1V1=T2P2V2

T2=P