Thermal Properties of Matter Questions

A black body at $1227^{\circ }\text{C}$ emits radiations with maximum intensity at a wavelength of $5000\text{A˚}$. If the temperature of the body is increased by $1000^{\circ }\text{C}$, the maximum intensity will be observed at:

Coefficient of linear expansion of brass and steel rods are ${\alpha }_1$ and ${\alpha }_2$. Lengths of brass and steel rods are $l_1$ and $l_2$ respectively. If $(l_2-l_1)$ is maintained same at all temperatures, which one of the following relations holds good?

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?

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 and all energy of ice gets converted into heat during its fall. The value of $h$ is: [Latent heat of ice is $3.4\times 10^5\text{J/kg}$ and $g=10\text{N/kg}$ ]