Thermal Properties of Matter PYQs

Three identical heat conducting rods are connected in series as shown in the figure. The rods on the sides have thermal conductivity 2K while that in the middle has thermal conductivity K. The left end of the combination is maintained at temperature 3T and the right end at T. The rods are thermally insulated from outside. In steady state, the temperature at the left junction is $T_1$ and that at the right junction is $T_2$. The ratio $T_1$/$T_2$ is

A cup of coffee cools from $90^\circ C$ to $80^\circ C$ in $t$ minutes, when the room temperature is $20^\circ C$. The time taken by a similar cup of coffee to cool from $80^\circ C$ to $60^\circ C$ at the same room temperature of $20^\circ C$ is:

The quantities of heat required to raise the temperature of two solid copper spheres of radii r₁ and r₂ (r₁ = 1.5 r₂) through 1 K are in the ratio :

An object kept in a large room having air temperature of 25°C takes 12 minutes to cool from 80°C to 70°C. The time taken to cool for the same object from 70°C to 60°C would be nearly:

Two rods $A$ and $B$ of different materials are welded together as shown in the figure. Their thermal conductivities are $K_1$ and $K_2$. The thermal conductivity of the composite rod will be:

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

A body cools from a temperature $3T$ to $2T$ in 10 minutes. The room temperature is $T$. Assume that Newton’s law of cooling is applicable. The temperature of the body at the end of the next 10 minutes will be:

The value of coefficient of volume expansion of glycerin is $5\times10^{-4}\,\text{K}^{-1}$. The fractional change in the density of glycerin for a rise of $40^{\circ}\text{C}$ in its temperature is:

Steam at $100^{\circ}\mathrm{C}$ is passed into $20\,\mathrm{g}$ of water at $10^{\circ}\mathrm{C}$. When the water acquires a temperature of $80^{\circ}\mathrm{C}$, the mass of water present will be: (Take specific heat of water $= 1\,\mathrm{cal\,g^{-1}\,^{\circ}C^{-1}}$ and latent heat of steam $= 540\,\mathrm{cal\,g^{-1}}$)

A quantity of water cools from $70^{\circ}\mathrm{C}$ to $60^{\circ}\mathrm{C}$ in the first $5$ minutes and to $54^{\circ}\mathrm{C}$ in the next $5$ minutes. The temperature of the surroundings is:

A piece of iron is heated in a flame. It first becomes dull red then reddish yellow and finally turns to white hot. The correct explanation for the above observation is possible by using

A slab of stone of area 0.36 m² and thickness 0.1 m is exposed on the lower surface to steam at 100°C. A block of ice at 0°C rests on the upper surface of the slab. In one hour 4.8 kg of ice is melted. (Given latent heat of fusion of ice = 3.36 × 10$^5$ J kg⁻¹) The thermal conductivity of slab is:

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

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

Which of the following circular rods, each made of the same material and whose ends are maintained at the same temperature difference, will conduct most heat?