If a black body emits $0.5 \ J$ of energy per second when it is at $27^{\circ} C$,then the amount of energy emitted by it when it is at $627^{\circ} C$ will be (in $J$)

The power radiated by a black body is $P$ and it radiates maximum energy at wavelength $\lambda_0$. If the temperature of the black body is now changed so that it radiates maximum energy at wavelength $\frac{3}{4}\lambda_0$,the power radiated by it becomes $nP$. The value of $n$ is

$A$ black coloured solid sphere of radius $R$ and mass $M$ is inside a cavity with vacuum inside. The walls of the cavity are maintained at temperature $T_0$. The initial temperature of the sphere is $3T_0$. If the specific heat of the material of the sphere varies as $\alpha T^3$ per unit mass with the temperature $T$ of the sphere,where $\alpha$ is a constant,then the time taken for the sphere to cool down to temperature $2T_0$ will be ($\sigma$ is Stefan-Boltzmann constant).

Assuming the Sun to be a spherical body of radius $R$ at a temperature of $T \ K$,evaluate the total radiant power incident on Earth at a distance $r$ from the Sun. Where $r_0$ is the radius of the Earth and $\sigma$ is Stefan's constant.

Three large identical plates are kept parallel to each other. The outer two plates are maintained at temperatures $T$ and $2T$, respectively. The temperature of the middle plate in steady state will be close to ........... $T$.

The surface of a black body is at a temperature $727^{\circ} C$ and its cross-section is $1 \,m^2$. Heat radiated from this surface in one minute in joules is (Stefan's constant $=5.7 \times 10^{-8} \,W / m^2 / K^4$ )