Thermal properties of matter practice · Medium

The length of a metal rod at ${0^0}C$ is $0.5\,m$. When it is heated, its length increases by $2.7\,mm$. The final temperature of rod is $\left[ {\alpha = 90 \times {{10}^{ - 61}}^0C} \right]$

Two cylinders P and Q have the same length and diameter and are made of different materials having thermal conductivities in the ratio 2:3. These two cylinders are combined to make a cylinder. One end of P is kept of ${100^0}C$ and another end of Q at ${0^0}C$. The temperature at the interface of P and Q is

The wavelength of the radiation emitted by a body depends upon

The tungsten filament of an electric lamp has a surface $A$ area and a power rating $P$. If the emissivity of the filament is $\varepsilon$ and $\sigma$ is Stefan’s constant, the steady temperature of the filament will be

A particular star (assuming it as a block body has a surface temperature of about $5 \times {10^4}K.$ The wavelength in nanometers at which its radiation becomes maximum is $(b = 0.0029\,\,mk)$

Assertion (A): At constant temperature, when pressure of a gas is increased by $10 \%$, then volume decreases by less than $10 \%$
Reason (R): At constant temperature the volume of gas is inversely proportional to the pressure acting on it.

(A): Two bodies at different temperatures, if brought in thermal contact do not necessary settle to the mean temperature.
(R): The two bodies may have different thermal capacities.

Heat is associated with

In an isochoric process if ${T_1} = {27^\mathrm{o}}C\mathrm{ }\,\,\,\mathrm{and}\,\,\,\mathrm{ }{T_2} = {127^\mathrm{o}}C$, then ${P_1}/{P_2}$ will be equal to

Assertion (A): Sometimes water pipes burst in severe winter.
Reason (R): On freezing water expands due to anamolous expansion.

Estimate the rate at which ice would melt in a wooden box $2.0 \mathrm{~cm}$ thick and of inside measurements $200 \mathrm{~cm} \times 120 \mathrm{~cm} \times 120 \mathrm{~cm}$ assuming that the external temperature is $30^{\circ} \mathrm{C}$ and coefficient of thermal conductivity of wood is $0.0004 \mathrm{~cal} \mathrm{~s}^{-1} \mathrm{~cm}^{-1}{ }^{\circ} \mathrm{C}$.

The latent heat of vaporization of a substance is always

The normal body-temperature of a person is $97^{\circ} \mathrm{F}$. Calculate the rate at which heat is flowing out of his body through the clothes assuming the following values. Room temperature $=47^{\circ} \mathrm{F}$, surface of the body under clothes $=1.6 \mathrm{~m}^2,$ conductivity of the cloth $=0.04 \mathrm{~J} \mathrm{~s}^{-1} \mathrm{~m}^{-1}{ }^{\circ} \mathrm{C}^{-1}$, thickness of the cloth $=0.5 \mathrm{~cm}$.

The temperature of body is increased from $27^{\circ} \mathrm{C}$ to $127^{\circ} \mathrm{C}$. The radiation emitted by it increases by a factor of

Two thermometers are used to record the temperature of a room. If the bulb of one is wrapped in wet hanky

Two litre glass flask contains some mercury. It is found that at all temperatures the volumes of the air inside the flask remains the same. The volume of the mercury inside the flask is
$\left( {\alpha \,\,\mathrm{for}\,\,\mathrm{glass}\, = \,9 \times {{10}^{ - 6}}/^\circ C,\,\,\gamma \,\,\mathrm{for}\,\,\mathrm{mercury}\, = \,1.8 \times {{10}^{ - 4}}/^\circ C} \right)$

A metal block of density $6000 \mathrm{~kg} \mathrm{~m}^{-3}$ and mass $1 \cdot 2 \mathrm{~kg}$ is suspended through a spring of spring constant $200 \mathrm{~N} \mathrm{~m}^{-1}$. The spring-block system is dipped in water kept in a vessel. The water has a mass of $260 \mathrm{~g}$ and the block is at a height $40 \mathrm{~cm}$ above the bottom of the vessel. If the support to the spring is broken, what will be the rise in the temperature of the water. Specific heat capacity of the block is $250 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$ and that of water is $4200 \mathrm{~J} \mathrm{~kg}^{-1} \mathrm{~K}^{-1}$. Heat capacities of the vessel and the spring are negligible.

If a body coated black at $600 \mathrm{~K}$ surrounded by atmosphere at $300 \mathrm{~K}$ has cooling rate $r_0$, the same body at $900 \mathrm{~K}$, surrounded by the same atmosphere, will have cooling rate equal to

A black body emits heat at the rate of $20 \mathrm{~W}$. When its temperature is $727^{\circ} \mathrm{C}$. Another black body emits heat at the rate of $15 \mathrm{~W}$, when its temperature is $227^{\circ} \mathrm{C}$. Compare the area of the surface of the two bodies, if the surrounding is at NTP.

(A): Cooking food is difficult on hills.
(R): The boiling point decreases with increases in pressure

A cube of a substance of coefficient of cubical expansion $\gamma_1$ is floating in a liquid of coefficient of cubical expansion $\gamma_2\left(\gamma_2 < \gamma_1\right)$, such that $50 \%$ of its volume is inside the liquid. If temperature of the system is now increased, the percentage of volume of cube inside the liquid may be

A large steel wheel is to be fitted on to a shaft of the same material. At $27^{\circ} \mathrm{C}$, the outer diameter of the shaft is $8.70 \mathrm{~cm}$ and the diameter of the central hole in the wheel is $8.69 \mathrm{~cm}$. The shaft is cooled using 'dry ice' (solid carbon dioxide). At what temperature of the shaft does the wheel slip on the shaft? Assume coefficient of linear expansion of the steel to be constant over the required temperature range. $\alpha_{\text {steel }}=1.20 \times 10^{-5} \mathrm{~K}^{-1} .$

A solid sphere of radius $\mathrm{R}$ and a hollow sphere of inner radius $\mathrm{r}$ and outer radius $\mathrm{R}$ made of copper are heated to the same temperature and are allowed to cool in the same environment. Then, choose the CORRECT statement :-

Assertion: Radiation is the speediest mode of heat transfer.
Reason: Radiation can be transmitted in zig-zag motion.

Statement A: Greater the mass of radiating body, slower will be cooling
Statement B: Greater the temperature of the surroundings, lower will be cooling

An ideal gas equation can be written as $P=\frac{\rho R T}{M_0}$ where $\rho$ and $M_0$ are respectively

A real gas can be approximated to an ideal gas at

Volume of gas becomes four times if

Assertion: The amount of radiation from sun's surface varies as the fourth power of its absolute temperature.
Reason: The sun is black body.

Assertion (A): Solids expands on heating
Reason (R): Atoms of the solid are an harmonic oscillators