Initial pressure and volume of a gas are ' P ' and ' $V$ ' respectively. First its volume is expanded to ' 4 V ' by isothermal process and then again its volume is reduced to ' V ' by adiabatic process then its final pressure if $\left(\gamma=\frac{3}{2}\right)$

The P-V diagrams for particular gas of different thermodynamic processes are given by

An ideal gas $(\gamma=1.5)$ is expanded adiabatically. To reduce root mean square velocity of molecules two times, the gas should be expanded

A black body radiates power ' P ' and maximum energy is radiated by it at a wavelength $\lambda_0$. The temperature of the black body is now so changed that it radiates maximum energy at the wavelength $\frac{\lambda_0}{4}$. The power radiated by it at new temperature is