Question

It can be shown that for a simple compressible substance, the relationship

cp - cv = - T \(\left(\cfrac{∂V}{∂T}\right)^2_p\)\(\left(\cfrac{∂p}{∂v}\right)_T\) exists

where c_p and c_v 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 ? 

(a) c_p is always greater than c_v 

(b) The right side of the equation reduces to R for an ideal gas

(c) Since \(\left(\cfrac{∂p}{∂v}\right)_T\) can be either positive or negative, and \(\left(\cfrac{∂V}{∂T}\right)_p\) must be positive, T must have a sign which is opposite to that of \(\left(\cfrac{∂p}{∂v}\right)_T\)

(d) c_p is very nearly equal to c_v for liquid water.

Answer 1

(b) The right side of the equation reduces to R for an ideal gas