# An amount Q of heat is added to a mono atomic ideal gas in a process in which the gas performs a work Q/2 on its surrounding .find equation of the process?

Mar 2, 2018

$T {V}^{\frac{1}{3}} = \setminus m b \otimes \left\{c o n s \tan t\right\}$

#### Explanation:

For an infinitesimal process
$\mathrm{dU} = \frac{3}{2} n R \mathrm{dT} = \delta Q - p \mathrm{dV} = \delta Q - \frac{\delta Q}{2} = \frac{\delta Q}{2} = \frac{1}{2} p \mathrm{dV}$

Using $p V = n R T$, this can be rewritten as

$\frac{3}{2} n R \mathrm{dT} = \frac{1}{2} \frac{n R T}{V} \mathrm{dV} \implies \frac{\mathrm{dT}}{T} = \frac{1}{3} \frac{\mathrm{dV}}{V} \implies$

$T {V}^{\frac{1}{3}} = \setminus m b \otimes \left\{c o n s \tan t\right\}$