Question

For perfect gas, the ratio of volume coefficient of expansion to pressure coefficient is :

• A. equal to one
• B. less than one
• C. more than one
• D. an imaginary quantity

Answer 1

Answer: (A)

equal to one

The volume coeffecient of expansion is given by ${\alpha }_v=\frac{1}{V}{\left(\frac{\partial V}{\partial T}\right)}_p$.
Now, PV = nRT
$\ln V=\ln T+\ln \frac{nR}{P}$
Differenciating with respect to T we get,
$\frac{1}{V}\left(\frac{\partial V}{\partial T}\right)=\frac{1}{T}$
${\alpha }_v=\frac{1}{T}$
Similarly, keeping volume constant we get,
${\alpha }_p=\frac{1}{T}$
Hence, the ratio is 1.