Embibe Experts Solutions for Chapter: Thermal Properties of Matter, Exercise 1: JEE Advanced Paper 2 - 2014

A container with $1 \mathrm{kg}$ of water in it is kept in sunlight, which causes the water to get warmer than the surroundings. The average energy per unit time per unit area received due to the sunlight is $700 \mathrm{W} {\mathrm{m}}^{-2}$ and it is absorbed by the water over an effective area of $0.05 {\mathrm{m}}^2.$ Assuming that the heat loss from the water to the surroundings is governed by Newton's law of cooling, the difference (in ${}^{\circ }\mathrm{C}$) in the temperature of water and the surroundings after a long time will be_________. (Ignore effect of the container, and take constant for Newton's law of cooling $=0.001 {\mathrm{s}}^{-1},$ Heat capacity of water $=4200 \mathrm{J} {\mathrm{kg}}^{-1} {\mathrm{K}}^{-1}$)

(Approximate the answer to two decimal place)

The ends Q and R of two thin wires, PQ and RS, are soldered (joined) together. Initially each of the wires has a length of $1 \mathrm{m}$ at $10°\mathrm{C}.$ Now the end P is maintained at $10°\mathrm{C},$ while the end S is heated and maintained at $400°\mathrm{C}.$ The system is thermally insulated from its surroundings. If the thermal conductivity of wire PQ is twice that of the wire RS and the coefficient of linear thermal expansion of PQ is $1.2\times {10}^{-5} {\mathrm{K}}^{-1},$ the change in length of the wire PQ is

A small object is placed at the centre of a large evacuated hollow spherical container. Assume the container is maintained at $0 \mathrm{K}$. At time $t=0$, the temperature of the object is $200 \mathrm{K}$. The temperature of the object becomes $100 \mathrm{K}$ at $t=t_1$ and $50 \mathrm{K}$ at $t=t_2$. Assume the object and the container to be ideal black bodies. The heat capacity of the object does not depend on temperature. The ratio $\left(\frac{t_2}{t_1}\right)$ _________ .

The filament of a light bulb has surface area $64 {\mathrm{mm}}^2.$ The filament can be considered as a black body at temperature $2500 \mathrm{K}$ emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of $100 \mathrm{m}$. Assume the pupil of the eyes of the observer to be circular with radius $3 \mathrm{mm}$. Then:

(Take Stefan-Boltzmann constant $=5.67\times {10}^{-8} \mathrm{W} {\mathrm{m}}^{-2} {\mathrm{K}}^{-4},$ Wiens' displacement constant $=2.90\times {10}^{-3} \mathrm{m} \mathrm{K}$, Planck's constant $=6.60\times {10}^{-34} \mathrm{J} \mathrm{s}$, speed of light in vacuum $=3.00\times {10}^8 \mathrm{m}{\mathrm{s}}^{-1}$)

A current carrying wire heats a metal rod. The wire provides a constant power $\left(\mathrm{P}\right)$ to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature $\left(\mathrm{T}\right)$ in the metal rod changes with time $\left(\mathrm{t}\right)$ as: $\mathrm{T}\left(\mathrm{t}\right)={\mathrm{T}}_0\left(1+\mathrm{\beta }{\mathrm{t}}^{\frac{1}{4}}\right)$
, where $\mathrm{\beta }$ is a constant with appropriate dimension while ${\mathrm{T}}_0$ is a constant with dimension of temperature. The heat capacity of the metal is:

A liquid at ${30\mathrm{ }}^{\mathrm{o}}\mathrm{C}$ is poured very slowly into a Calorimeter that is at temperature of ${110\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$ The boiling temperature of the liquid is ${80\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$ It is found that the first $5\mathrm{ }\mathrm{g}\mathrm{m}$ of the liquid completely evaporates. After pouring another $80\mathrm{ }\mathrm{g}\mathrm{m}$ of the liquid the equilibrium temperature is found to be ${50\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$ The ratio of the Latent heat of the liquid to its specific heat will be ______ ${\mathrm{ }}^{\mathrm{o}}\mathrm{C}.$

[Neglect the heat exchange with surrounding]

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures $T_1=300 \mathrm{K} \mathrm{a}\mathrm{n}\mathrm{d} T_2=100 \mathrm{K}$ as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are $K_1 \mathrm{a}\mathrm{n}\mathrm{d} K_2$, respectively. If the temperature at the junction of the two cylinders in the steady state is $200\mathrm{ }\mathrm{K}$, then $K_1/K_2$ is

A human body has a surface area of approximately $1\mathrm{ }{\mathrm{m}}^2$. The normal body temperature is $10\mathrm{ }\mathrm{K}$ above the surrounding room temperature $T_0$ . Take the room temperature to be $T_0=300 \mathrm{K}$ . For $T_0=300 \mathrm{K}$, the value of $\sigma T^4=460 \mathrm{W} {\mathrm{m}}^{-2}$(where $\sigma$ is the Stefan-Boltzmann constant). Which of the following options is/are correct?