Statement (I): The Clapeyron equation enables us to determine the enthalpy change associated with phase change.

Statement (II): Using usual notations, the Clapeyron equation is given by \({\left( {\frac{{dT}}{{dP}}} \right)_{sat}} = \frac{{{h_{fg}}}}{{T{v_{Fg}}}}\)

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  1. Both Statement (I) and Statement (II) are individually true and Statement (II) is the correct explanation of Statement (I)
  2. Both Statement (I) and Statement (II) are individually true but Statement (II) is NOT the correct explanation of Statement (I)
  3. Statement (I) is true but Statement (II) false
  4. Statement (I) is false but Statement (II) is true

Answer (Detailed Solution Below)

Option 3 : Statement (I) is true but Statement (II) false
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Detailed Solution

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Concept:

Clausius-Clapeyron equation:

Clausius-Clapeyron equation is a relationship between the enthalpy of evaporation, saturation pressure and temperature, and the specific volume of the two phases involved.

F3 M.J Madhu 17.04.20 D 3

This equation can be derived from Maxwell equation:

\({\left( {\frac{{\partial P}}{{\partial T}}} \right)_v} = {\left( {\frac{{\partial s}}{{\partial v}}} \right)_T}\)

P is the pressure, T is the temperature, v is the specific volume and s is the specific entropy

During a phase change, the pressure and temperature are dependent properties

\({\left( {\frac{{dP}}{{dT}}} \right)_v} = {\left( {\frac{{ds}}{{dV}}} \right)_T}\)

During phase change \({s_{fg}} = \frac{{{h_{fg}}}}{{{T_{sat}}}}\)

\(\frac{{dP}}{{dT}} = \frac{{{s_g} - {s_f}}}{{{v_g} - {v_f}}} = \;\frac{{{h_{fg}}}}{{{T_{sat}}{v_{fg}}}}\)

This equation is useful to find out the latent heat (enthalpy change hfg) at the change of phase for a given pressure.

Therefore statement II) is incorrect as it has represented the Clausius-Clapeyron equation in the wrong way.  

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