A gas is initially at a pressure of 100 kPa and its volume is 2.0 m3. Its pressure is kept constant and the volume is changed from 2.0 m3 to 2.5 m3. Its volume is now kept constant and the pressure is increased from 100 kPa to 200 kPa. The gas is brought back to its initial state, the pressure varying linearly with its volume.
(a) Whether the heat is supplied to or extracted from the gas in the complete cycle?
(b) How much heat was supplied or extracted?
From graph
Va=2m3
Vb=Vc=2.5m3
Pa=Pb=100kPa=100
103Pa
Pc=200kPa=200
103Pa
Work done in process ABCA = area enclosed by the triangle ABC
ΔW =0.5×BC×AB
Where BC= height of the triangle
AB= base of triangle
So,
ΔW=0.5×(200-100)×103
(2.5-2)
ΔW=0.5×100×0.5×103 =25000J
a) Process ABCA is a cyclic process. The system is brought back to its initial state. Since internal energy is a state function, change in internal energy will be zero.
So, ΔU=0
From first law of thermodynamics, we know that,
ΔQ=ΔU+ΔW
Where ΔQ=heat supplied to the system
ΔU=change in internal energy
ΔW=work done by the system
∴ ΔQ=ΔW=25000J
Since work done is positive, work is done by the gas. When work is done by the gas heat is supplied to the system.
b) Amount of heat supplied = work done by the gas in the cyclic process
∴ ΔQ=ΔW=25000J.