Question

A monoatomic ideal gas follows the process:

${\text{TV}}^{\frac{3}{2}}=\text{constant}$

The molar specific heat for this process is $\left(\frac{5R}{y}\right)$, where R is gas constant. Then the value of ‘y’ is ___ .

Answer 1

${\text{TV}}^{\frac{3}{2}}=\text{constant}$

$\Rightarrow \frac{\left(\text{PV}\right){\text{V}}^{\frac{3}{2}}}{\text{nR}}=\text{constant}$

$\Rightarrow {\text{PV}}^{\frac{5}{2}}=\text{constant}$

${\text{PV}}^x=\text{constant}$

$x=\frac{5}{2}$

$\text{C}={\text{C}}_v+\frac{\text{R}}{1-x}$

$\text{C}=\frac{3}{2}\text{R}+\frac{\text{R}}{1-\frac{5}{2}}$

$\text{C}=\frac{5R}{6}$