Embibe Experts Solutions for Chapter: Thermal Properties of Matter, Exercise 2: Exercise 2

The total radiant energy per unit area, 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 $T \mathrm{K}$ is given by

(where $\sigma$ is Stefan's constant)

An aluminium sphere of $20 \mathrm{cm}$ diameter is heated from $0°\mathrm{C}$ to $100°\mathrm{C}$. Its volume changes by (given that coefficient of linear expansion for aluminium ${\mathrm{\alpha }}_{\mathrm{Al}}=23\times {10}^{-6} {}^{\circ }\mathrm{C}^{-1}$)

A piece of ice (heat capacity $=2100 \mathrm{J} {\mathrm{kg}}^{-1} °{\mathrm{C}}^{-1}$ and latent heat $=3.36\times {10}^5 \mathrm{J} {\mathrm{kg}}^{-1}$ ) of mass $m$ grams is at $-5°\mathrm{C}$ at atmospheric pressure. It is given $420 \mathrm{J}$ of heat so that the ice starts melting. Finally, when the ice-water mixture is in equilibrium, it is found that $1 \mathrm{g}$ of ice has melted. Assuming there is no other heat exchange in the process, the value of $m$ is

A student takes $50 \mathrm{g}$ wax (specific heat$\left.=0.6 \mathrm{kcal} \mathrm{kg} °\mathrm{C}\right)$ and heats it till it boils. The graph between temperature and time is as follows. Heat supplied to the wax per minute and boiling point are respectively

The graph represents

The plots of intensity versus wavelength for three black bodies at temperatures $T_1,T_2$ and $T_3$ respectively are as shown. Their temperature is such that

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

If the radius of a star is $R$ and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is $Q$?