The energy spectrum of a black body exhibits a maximum of wavelength $\lambda_0$. The temperature of the black body is now changed such that the energy is maximum at wavelength $\dfrac{3\lambda_0}{2}$. The ratio of power radiated by the black body will be

An ideal gas undergoes cyclic process ABCDA as shown in given p-V diagram. What is the magnitude of amount of work done by the gas?

Two samples A and B of gas initially at the same pressure and temperature. They are compressed from volume $V$ to $\dfrac{V}{2}$ (A isothermally and B adiabatically). The relation between pressure of the gas A ($P_A$) and pressure of gas B ($P_B$) is

A vessel has $6$ gram of hydrogen at pressure $P$ and temperature $500$ K. A small hole is made in it so that hydrogen leaks out. How much hydrogen leaks out if the final pressure is $\dfrac{P}{2}$ and the temperature falls to $300$ K?