A black body is at a temperature of $5760 \text{ K}$. The energy of radiation emitted by the body at wavelength $250 \text{ nm}$ is $U_1$, at wavelength $500 \text{ nm}$ is $U_2$ and that at $1000 \text{ nm}$ is $U_3$. Wien's constant, $b = 2.88 \times 10^6 \text{ nm K}$. Which of the following is correct?

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

A piece of ice falls from a height $h$ so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice. The value of $h$ is: [Latent heat of ice is $3.4 \times 10^5 \text{ J/kg}$ and $g = 10 \text{ N/kg}$]

A black body at $227^\circ\text{C}$ radiates heat at the rate of $7 \text{ cal cm}^{-2}\text{s}^{-1}$. At a temperature of $727^\circ\text{C}$, the rate of heat radiated in the same units will be:

A copper rod of $88 \text{ cm}$ and an aluminium rod of an unknown length have an equal increase in their lengths independent of an increase in temperature. The length of the aluminium rod is: ($\alpha_{\text{Cu}} = 1.7 \times 10^{-5} \text{ K}^{-1}$ and $\alpha_{\text{Al}} = 2.2 \times 10^{-5} \text{ K}^{-1}$)

A black body at $227^{\circ}\text{C}$ radiates heat at the rate of $7\text{ cal cm}^{-2}\text{s}^{-1}$. At a temperature of $727^{\circ}\text{C}$, the rate of heat radiated in the same units will be

The two ends of a rod of length $L$ and a uniform cross-sectional area $A$ are kept at two temperatures $T_1$ and $T_2$ ($T_1 > T_2$). The rate of heat transfer $\frac{dQ}{dt}$ through the rod in a steady state is given by:

Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at $100^{\circ}\text{C}$, while the other one is at $0^{\circ}\text{C}$. If the two bodies are brought into contact, then assuming no heat loss, the final common temperature is -

The total radiant energy per unit area per unit time, normal to the direction of incidence, received at a distance $R$ from the centre of a star of radius $r$, whose outer surface radiates as a black body at a temperature $T\text{ K}$ is given by (where $\sigma$ is Stefan's constant):