Thermal properties of matter practice · Mixed difficulty

Assertion: A sphere a cube and a thin circular plate made of same material and of stable mass are initially heated to $200^{\circ} \mathrm{C}$, the plate will cool at fastest rate.
Reason: Rate of cooling $=\frac{\mathrm{eA} \sigma}{\mathrm{ms}}\left(\mathrm{T}^4-\mathrm{T}_0^4\right) \propto$ surface area and surface area is maximum for plate.

(A): Specific heat is known as thermal inertia.
(R): The body having higher specific heat cools very slowly and gets heated up very slowly and vice versa

A spherical black body with a radius of $12\;\mathrm{ cm}$ radiates $\mathrm{450\; Watt}$ power at $\mathrm{500\; K}\mathrm{.}$If the radius were halved and the temperature doubled, the power radiated in watt would be

Two spheres $P$ and $Q$ , of same colour having radii 8 cm and 2 cm are maintained at temperatures ${127^0}C$ and ${527^0}C$ respectively. The energy radiated by $P$ and $Q$ is

A piece of metal weighs $45g$ in air and $25g$ in a liquid of density $1.5 \times {10^3}kg - {m^{ - 3}}$ kept at ${30^0}C$ . When the temperature of the liquid is raised to ${40^0}C$ , the metal piece is weighs $27g$. The density of liquid at ${40^0}C$, is $1.25 \times {10^3}kg - {m^{ - 3}}$. The coefficient of linear expansion of metal is

Assertion (A) : A normal body can radiate energy more than a perfectly black body.

Reason (R) : A perfectly black body is always black in colour.

A: Liquid molecules have greater potential energy at the melting point
R: Intermolecular spacing between molecules increase at melting point

For an ideal conductor, thermal resistance is

A uniform cylinder of steel of mass ${M}$, radius ${R}$ is palced on frictionless bearings and set to rotate about vertical axis with angular velocity $\omega_0$. After the cylinder has reached the specified state of rotation it is heated without any mechanical contact from temperature $T_0$ to $T_0+\Delta T$. If $\frac{\Delta I}{I}$ is the fractional change in moment of inertia of the cylinder and $\frac{\Delta \omega}{\omega_0}$ be the fractional change in the angular velocity of the cylinder and $\alpha$ be the coefficient of linear expansion, then

A brass rod and lead rod each $80 \mathrm{~cm}$ long at $0^{\circ} \mathrm{C}$ are clamped together at one end with their free ends coinciding. If the system is placed in a steam bath then the separation of free ends of the rods is:

$\left(\alpha_{\text {Brass}}=18 \times 10^{-6} /{ }^{\circ} \mathrm{C} \text { and } \alpha_{\text {Lead}}=28 \times 10^{-6} /{ }^{\circ} \mathrm{C}\right)$

Total random kinetic energy of the molecules in 1 mole of a gas at a temperature of 300 K is $\left[ {R = 2\,\,\,{\text{cal/mole}}\,\,\,^\circ C} \right]$

If thermal conductivity of rod is 4, then its thermal resistivity will be

$25 \mathrm{gm}$ water is filled in a vessel of water equivalent $5 \mathrm{gm}$ at $70^{\circ} \mathrm{C}$ then find out the $T_{\text {mix }}$ when $20 \mathrm{gm}$ of water at $0^{\circ} \mathrm{C}$ is mixed.

(A): The radiation from the sun's surface varies as the fourth power of its absolute temperature.
(R): The sun is not a black body.

Statement 1: When two liquid samples of different masses with temperatures $T_1$ and $T_2 \,\left(T_1 < T_2\right)$ but same specific heats are mixed the equilibrium temperature of the mixture is $\frac{T_1+T_2}{2}$
Statement 2: The amount of heat lost by the hotter liquid is equal to the amount of heat absorbed by the cooler liquid.

The temperature of a gas contained in a closed vessel of constant volume increases by 1$^ \circ C$ when the pressure of the gas is increased by 1%. The initial temperature of the gas is

Water has maximum density at

A flask of mercury is sealed off at $20^{\circ} \mathrm{C}$ and is completely filled with mercury. If the bulk modulus for mercury is 2500 $\mathrm{MPa}$ and the coefficient of volume expansion of mercury is $1.82 \times 10^{-4 /} \mathrm{C}$ and the expansion of glass is ignored, the pressure of mercury within the flask at $100^{\circ} \mathrm{C}$ will be

A body cools from $75^{\circ} \mathrm{C}$ to $72^{\circ} \mathrm{C}$ in time $t_1$ from $72^{\circ} \mathrm{C}$ to $69^{\circ} \mathrm{C}$ in $t_2$ and from $69^{\circ} \mathrm{C}$ to $66^{\circ} \mathrm{C}$ in ${t}_3$, then

Statement 1: Change of state is an example of isothermal process.
Statement 2: Change of state from solid to liquid occurs only at melting point of solid and change of state from liquid to gas occurs only at boiling point of liquid. Thus, there is no change of temperature during change of state.

The coefficient of apparent expansion of a liquid is $\mathrm{C}$ when heated in a copper vessel and it is $S$ when heated in a silver vessel. If $A$ is the coefficient of linear expansion of copper, then that of silver is :

Two spheres are made of same metal and have same mass. One is solid and the other is hollow. When heated to the same temperature, which of the following statements is correct about the percentage increase in their diameters.

The capacity of a vessel is 3 litres. It contains $6 \mathrm{~g}$ oxygen, $8 \mathrm{~g}$ nitrogen and $5 \mathrm{~g}\,\, \mathrm{CO}_2$ mixture at $27^{\circ} \mathrm{C}$. If $\mathrm{R}=8.31 \mathrm{~J} / \mathrm{mole} \times$ kelvin, then the pressure in the vessel in $\mathrm{N} / \mathrm{m}^2$ will be (approx.) :-

Statement A: The radiation from the sun surface varies as the fourth power of its absolute temperature.
Statement B: Sun is not a black body.

Density of a substance at ${0^0}C$ is 10.6 gm/c.c and at ${100^0}C$ is 10 gm/c.c. Coefficient of linear expansion of solid is

Statement 1: At room temperature ice does not sublimate from ice to steam.
Statement 2: The critical point of water is much above the room temperature.

A centigrade and a Fahrenheit thermometer are dipped in boiling water. The water temperature is lowered until the Fahrenheit thermometer registers ${140^0}$. What is the fall in temperature as registered by the Centigrade thermometer

Assertion (A): A man would feel iron or wooden balls equally hot at $98.4^{\circ} \mathrm{F}$
Reason (R): At $98.4^{\circ} \mathrm{F}$ both iron and wood have same thermal conductivity.

Which of the following instrument is used measure temperature of the source from its thermal radiations?

Assertion (A): $P V / T=$ constant for 1 gram of gas. This constant varies from gas to gas
Reason (R): I gram of different gases at NTP occupy different volumes