Question

For an ideal gas the expression $[T{\left(\frac{\delta s}{\delta T}\right)}_P-T{\left(\frac{\delta s}{\delta T}\right)}_V]$ is always equal to

• A. $R$
• B. $RT$
• C. $\text{Zero}$
• D. $\frac{c_p}{c_v}$

Answer 1

The correct option is A $R$

$T{\left(\frac{\delta s}{\delta T}\right)}_P-T{\left(\frac{\delta s}{\delta T}\right)}_V=T\times \frac{c_p}{T}-T\frac{c_v}{T}$

$=c_p-c_v=R$

$\text{where}{\left(\frac{\delta s}{\delta T}\right)}_P=\frac{c_p}{T}\text{and}{\left(\frac{\delta s}{\delta T}\right)}_V=\frac{c_v}{T}$