A wire of length $L$ and diameter $d$ is used in a bulb. The temperature of wire is $T$ and power radiated by the wire is $P$. Its emissivity is ($\sigma$ = Stefan's constant) (Assume that emissivity of wire material is same at all wavelength)

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