Thermal Properties of Matter

Two different materials $M_1, M_2$ of equal dimensions (length $L$ and uniform cross-sectional area $A$) having thermal conductivities $k_1$ and $k_2$ respectively are connected together through a bolt $M_3$. The bolt…

An incandescent lamp of wattage $W$ is filled with argon gas and has a tungsten filament. The collision frequency of evaporated tungsten atoms with the argon atoms is found to be proportional to $W^\alpha$. The most…

The Parker solar probe, orbiting the Sun, experiences solar radiation flux of 650 $\mathrm{kW} \cdot \mathrm{m}^{-2}$. The heat shield (area $=1.0 \mathrm{~m}^2$, emissivity $=1.0$) surrounding the probe is internally…

In a room at temperature $20^{\circ} \mathrm{C}$, a cup of coffee cools from $80^{\circ}$ C to $75^{\circ} \mathrm{C}$ in 2 minutes. The time, in minutes, taken by the coffee to cool from $40^{\circ} \mathrm{C}$ to…

A solid sphere of uniform density and radius $R$ cools radiatively with a time constant $\tau$ as per the following expression: $T(t)=T_s+\left(T_h-T_s\right) e^{-t / \tau}$ where $T_h$ is the initial temperature of the…

A current I is passing flowing through a thin copper slab placed on a diamond slab. The bottom surface of the diamond slab is maintained at $0^{\circ} \mathrm{C}$ and the remaining arrangment is thermally insulated from…

A metal rod, connected between two high voltage electrodes, attains steady-state temperature through a balance between radiated power loss and Joule heating. The temperature of the surrounding is neglegible compared to…

A hot metal block at temperature $\theta_H$, kept in a room at lower temperature $\theta_R$, cools as per Newton's law of cooling. In 22 minutes, the difference of temperature with the room reduces to…

A star of radius $R_S$ and surface temperature of $T_S$, irradiates a planet of radius $R_E$. The distance between the star and the planet is $R_{S E}$. The average temperature $T_E$ on the surface of the planet can be…

A bimetallic strip of lead and nickel has a total thickness of $8 \mathrm{~cm}(4 \mathrm{~cm}$ each). The strip is straight at a temperature of 300 K . The coefficient of linear expansion of lead is $29 \times 10^{-6}…

Water and ice having equal masses are placed inside an insulated container. The initial temperatures of water and ice are $40^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$ respectively. The equilibrium temperature of…

A body, placed in vacuum, starts cooling from the initial temperature of $T_0 \mathrm{~K}$. Let $\Delta t$ be the time required to reduce the temperature to $T_0 / 2 \mathrm{~K}$. Then, the approximate time needed to…