Entropy and The Second Law of Thermodynamics
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Entropy Change for Irreversible Process: |
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The total entropy of an isolated system that undergoes a change can never decrease. If the
process is irreversible, then the total entropy of an isolated system always increases. However, the
total entropy of a reversible process remains constant. And the change in entropy of the universe
must be greater than zero for an irreversible process and equal to zero for a reversible process.
Let us consider an example of a system in which a hot reservoir and a cold reservoir in
thermal contact with each other and isolated from the rest of the universe. A process occurs during
which the energy Q is transferred by heat from the hot reservoir
at temperature Th to the cold
reservoir at temperature Tc. Since, the cold reservoir absorbs energy Q, its entropy increases by Q/Tc. At the same time, the hot reservoir loses energy Q and so its entropy change is
–Q/Th. Since, Th > Tc, the entropy of the cold reservoir is greater than the decrease in entropy of the hot reservoir. Thus,
the change in entropy of the system is given by,
In the adiabatic free expansion of a gas occupying an
initial volume Vi, when it expands
irreversibly to a volume Vf the entropy change of the
system is given as:
Here, the isothermal expansion of the gas is considered. Since Vf > Vi,
ΔS is positive.
Thus, the
entropy and disorder of the gas increase as a result of the irreversible adiabatic
expansion.
Similar to the examples given above let us consider a calorimetric process, where a
substance of
mass m1, specific heat c1,
and initial temperature T1 is placed in thermal contact with a second
substance of mass m2, specific heat c2
and initial temperature T2 > T1. The two
substances are
contained in a calorimeter so that no energy is lost to the surroundings. The system
of two
substances is allowed to reach thermal equilibrium. The total entropy change for the system is
given as:
Here Tf is given as:
The equation for entropy change in this irreversible process indicates that the
change in entropy is
positive and this equation is valid when no mixing of different substances occurs.
When, mixing is
allowed, the entropy further increases.
From all of these examples it can be concluded that
the entropy of the universe increases in
an irreversible process.
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