It can be shown that for a simple compressible substance, the relationship
Cp-Cv=-T(V/ T)2p( P/ v)T exists
Where Cp and Cv are specific heats at constant pressure and constant volume respectively
T is temperature, V is volume and P is pressure
Which one of the following statements is NOT true?
Option (A)
Cp is always greater than Cv
Option (B)
The right side of the equation reduces to R for an ideal gas
Since (P/ V)T can be either positive or negative and(v/ T)2P must be positive T must have a sign that is opposite to that of (P/ V)T
Cp is very nearly equal to Cv for liquid water
Correct Option:
Question Solution:
Cp -Cv = -T(v/T)2p(P/V)T
Since (v/T)2p is always positive and (P/V)T for any substance is negative, (Cp-Cv) is always positive. Therefore Cp is always greater then Cv
When (v/T)p =0 (for water at 4°C when density is maximum or specific volume minimum) Cp = Cv