Question

The Clausius-Clapeyron equation may be given as:
A. \[{\log _{10}}(\dfrac{{{P_2}}}{{{P_1}}}) = \dfrac{{\Delta {H_{vap}}}}{{2.303R}}[\dfrac{1}{{{T_1}}} - \dfrac{1}{{{T_2}}}]\]
B. \[\dfrac{{dP}}{{dT}} = \dfrac{{\Delta S}}{{\Delta V}}\]
C. \[\dfrac{{dP}}{{dT}} = \dfrac{q}{{T\Delta V}}\]
 D.\[\dfrac{{dP}}{{dT}} = \dfrac{{\Delta V}}{{\Delta S}}\]

Answer 1

Hint: This is a multiple choice question because there are more than one equations of Clauisus-Clapeyron. It tells the direct relation between pressure and latent heat.


Step by step answer:The Clausius-Clapeyron equation is named after Rudolf Clausius and Benoit Paul Clapeyron is a way of characterizing a discontinuous phase transition between two phases of matter of a single constituent.
On a given pressure temperature diagram, the line which separates two phases is called a coexistence curve. The Clausius-Clapeyron relation gives the slope of the tangents to this curve. Mathematically it can be given by following formulas,
 \[\dfrac{{dP}}{{dT}} = \dfrac{{\Delta S}}{{\Delta V}}\]
 \[\dfrac{{dP}}{{dT}} = \dfrac{q}{{T\Delta V}}\]
 \[{\log _{10}}(\dfrac{{{P_2}}}{{{P_1}}}) = \dfrac{{\Delta {H_{vap}}}}{{2.303R}}[\dfrac{1}{{{T_1}}} - \dfrac{1}{{{T_2}}}]\]
All these formulas are valid. In this formulas,
 \[\dfrac{{dP}}{{dT}}\] is the slope of the tangent to the coexistence curve at any point
 \[L\] is the specific latent heat
 \[T\] is the temperature
 \[\Delta V\] is the specific volume change of phase transition
 \[\Delta S\] is the specific entropy change of the phase transition.
Therefore, the correct options are A, B and C. All the three options are correct.

Additional Information: The Clausius-Clapeyron equation is derived from the first and second law of thermodynamics. It is the relationship between Vapour pressure and temperature. It mainly gives the relationship between the natural log of vapour pressure and the inverse of temperature and is a convenient way to measure the heat of vaporization in laboratory and to measure vapour pressure of a liquid at a temperature if the heat of vaporization and vapour pressure at one temperature are known.


Note: Please be clear that this equation is valid and applied for the processes where there is a change in phase.