Exercises

A solid sphere and a hollow sphere of the same material and of equal radii are heated to the same temperature.

Three identical conducting rods are connected as shown in the figure. Given that ${\mathrm{\theta }}_{\mathrm{a}}=40 °\mathrm{C}, {\mathrm{\theta }}_{\mathrm{c}}=30 °\mathrm{C}$ and ${\mathrm{\theta }}_{\mathrm{d}}=20 °\mathrm{C}$. Choose the correct options.

Two liquids of specific heat ratio $1: 2$ are at temperatures $2\mathrm{\theta }$ and $\mathrm{\theta }$.

Two conducting rods, when connected between two points at constant but different temperatures separately, the rate of heat flow through them are $q_1$ and $q_2$.

Choose the correct options.

A hot body placed in air is cooled according to Newton's law of cooling, the rate of decrease of temperature being $k$ times the temperature difference from the surroundings. Starting from $t=0$, find the time in which the body will lose half the maximum temperature it can lose.

Ice at $0 °\mathrm{C}$ is added to $200 \mathrm{g}$ of water, initially at $70 °\mathrm{C}$ in a vacuum flask. When $50 \mathrm{g}$ of ice has been added and has all melted, the temperature of the flask and contents is $40 °\mathrm{C}$. When a further $80 \mathrm{g}$ of ice has been added and has all melted, the temperature of the whole becomes $10 °\mathrm{C}$. Find the latent heat of fusion of ice.

A copper cube of mass $200 \mathrm{g}$ slides down a rough inclined plane of inclination $37°$ at a constant speed. Assuming that the loss in mechanical energy goes into the copper block as thermal energy, find the increase in temperature of the block as it slides down through $60 \mathrm{cm}$. Specific heat capacity of copper is equal to $420 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$. (Take $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)