Question

requirement and rational for transforming the clapeyron equation into clausius clapeyron equation

Answer 1

Solution:

Clayperon equation can be transformed to clausius-clayperon equation by adopting the ideal gas equation. Thus, clausius clayperon equation is obtained by liquid=vapor equilibrium.

For liquid vapor equilibrium:

Liquid ===== Vapor

Clayperon equation is written as,

dp /dT = ΔHv / T (Vg -Vl) -----(1)

Where,

dp = Change in pressure

dT = Change in temperature

ΔHv = heat of vaporization

Vg = Volume of gas

Vl = Volume of liquid

Since, Vg >>> Vl

Hence, Vl can be neglected from denominator. Thus, equation 1 can be written as,

dp/dT = ΔHv / T Vg

Vg = RT/P. (From ideal gas equation)

Thus,

dp/dT = ΔHv P/T x RT

dp/dT = .ΔHv x P / RT^2

dp / P = (dT/T^2) x ΔHv/R

ln P2/P1 = - (ΔHv /R) ( 1/T1 - 1/T2)

The above equation is known as Clausius-Clayperon equation.