Measurement of Entropy Change





For a reversible change at constant temperature the change in entropy is equal to heat absorbed or evolved divided by the constant temperature in Kelvin.

Thus,

\Delta S = \dfrac{q_{rev.}}{T}

 

The unit of entropy in J K mol^{-1}. The value of AS is positive if heat is absorbed and negative if heat is evolved. The entropy change in melting a solid can be calculated if enthalpy of fusion (\Delta H_{fusion}) is known.

\Delta S_{melt} = \dfrac{\Delta H_{fusion}}{T_{melt}}

 

Similarly, the entropy change for vaporisation of a liquid into its vapour at its boiling point can be calculated if enthalpy of vapourisation (\Delta H_{Vap.}) is known.

\Delta S_{vap.} = \dfrac{\Delta H_{vap.}}{T_{boiling}}

Similarly the entropy of sublimation is given as

\Delta S_{sub} = S_{Vapour}- S_{solid} = \dfrac{\Delta H_{Sub}}{T}

 

It is important to note that, the entropy change for a reaction carried out reversibly is different from a reaction carried out irreversibly. In other words, for an irreversible spontaneous change,

\Delta S > \dfrac{q}{T} \\[3mm] \Delta S > \dfrac{\Delta E + P \Delta V}{t} \\[3mm] \Delta S > 0

 

For a reversible change,

\Delta S = \dfrac{q}{T} = \dfrac{\Delta E + P \Delta }{T} \\[3mm] or \Delta S = 0

 

Entropy changes for Ideal gases:

 

(A)   For change of state: (Initial to final)

\Delta S = 2.303 n C_v \log_{10}[ \dfrac{T_2}{T_1} ] + 2.303 n R \log_{10} [ \dfrac{V_2}{V_1} ]

 

\Delta S = 2.303 n C_p \log_{10} [ \dfrac{T_2}{T_1} ] + 2.303 n R \log_{10}[ \dfrac{P_1}{P_2}]

 

(B)   For isothermal process:

\Delta S = 2.303 n R \log_{10} [\dfrac{V_2}{V_1}] or [\dfrac{P_1}{P_2}]

 

(C)   For Isochoric process:

\Delta S = 2.303 n C_v \log_{10}[\dfrac{T_2}{T_1}] or [\dfrac{P_1}{P_2}]

 

(D)   For Isobaric process:

\Delta S = 2.303 n C_p \log_{10} [\dfrac{T_2}{T_1} or [\dfrac{V_2}{V_1}]

 

Some examples of increase or decrease of entropy:

On stretching a rubber band the entropy decreases as the coiled macro molecule become un-coiled i.e. randomness in structure decreases.

 Increase of entropy losses:

On boiling an egg entropy increases as due to denaturation the helical structure of protein become more complicated and random coiled structure.

In a solution of H_2O + C_2H_5OH; \Delta S_{vap} is very high due to extensive H-bonding.

Trouton’s rule: According to .it \Delta S_{Vap} of most of the liquids is 88 \pm 5J / mole K at normal B.P.



Related posts:

  1. Physical significance of Entropy The entropy of a substance is real physical quantity and...
  2. Carbon Dating Carbon dating W.F. Libby (1950)has shown that by measuring the...
  3. Henderson’s Equation Henderson derived an equation to calculate the pH value of...
  4. Heat Content or Enthalpy When the change of state of a system is brought...
  5. Characterstics and Factors Influencing Equilibrium constant Characteristics of Equilibrium Constant 1. It has a definite value...