Question

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

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

Answer 1

Answer: (B)

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.