Subsystem 1 having a fluid of mass m
1 specific heat c
1 and temperature t
1 and subsystem 2 consisting of a fluid of mass m
2, specific heat c
2, and temperature t
2, comprise a composite system in an adiabatic enclosure figure. When the partition is removed, the two fluids mix together, and at equilibrium let t
f be the final temperature, and t
2 < t
f < t
1 Since energy interaction is exclusively confined to the two fluids, the system being isolated
∴
Entropy change for the fluid in subsystem1,
This will be negative, since T
1 > T
fEntropy change for the fluid in subsystem 2
This will be positive, since T
2 < T
f
ΔS
univ will be positive definite, and the mixing process is irreversible.
Although the mixing process is irreversible, to evaluate the entropy change for the subsystem, the irreversible path was replaced by a reversible path on which the integration was performed.