Two spherical black bodies of radius $\mathrm{R}_1$ and $\mathrm{R}_2$ with surface temperatures $\mathrm{T}_1$ and $\mathrm{T}_2$ respectively. If $T_1=2 T_2$ and they radiate the same power then relation between $R_1$ and $R_2$ is

In an adiabatic change, the pressure and temperature of a diatomic gas are related as $\mathrm{P} \propto \mathrm{T}^{\mathrm{c}}$, where c is a constant. The value of c is (consider gas molecules are rigid)

A system is compressed adiabatically, then its temperature

A blackbody at $1227^{\circ} \mathrm{C}$ emits radiation with maximum intensity at a wavelength of $5600 $$\mathop {\rm{A}}\limits^{\rm{o}} $. If the temperature of the body is increased by $1000^{\circ} \mathrm{C}$, the maximum intensity will be at wavelength