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Definition of Entropy

If any process is carried out reversibly, so that dqrev is the heat absorbed by the system in the process at constant temperature (T), then the entropy change (dS) is given by
Description: 45443.png
For finite changes,
Description: 45451.png

Calculation of entropy change

The entropy change for a given process is given by
Description: 45459.png
If we replace dq by an expression for the heat absorbed for a particular process, we can calculate the entropy change.
  • Heating of a solid: When only heat change is involved, as in the heating of a solid, the heat change is given by the expression
    Quantity of heat (q) = m × s × Δt
    where m is the mass, s the specific heat, and Δt the temperature rise.
    For one mole,
    dq = Cs × dT; Description: 45471.png
  • Change of state: There are changes taking place at constant temperatures (i.e., isothermal) during which the two states are at equilibrium with one another provided the process is carried out reversibly. The heat absorbed will be latent heat (L) and the temperature will be melting or boiling point.
    Description: 45481.png
  • Entropy change in ideal gas: For an ideal gas changing its state from (P1, V1, T1) to (P2, V2, T2),
    Description: 45491.png
    For an isothermal process (T2 = T1),
    Description: 45500.png
    For an isobaric process,
    Description: 45508.png
    For an isochoric process,
    Description: 45517.png
    For an adiabatic process,
    ΔS = 0 (since dq = 0)

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