Thermal properties of matter practice · Mixed difficulty

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

What is the percentage change in length of 1m iron rod if its temperature changes by ${100^ \circ }C\,$ $\left[ {\alpha \,\,\mathrm{for}\,\mathrm{iron}\, = \,2 \times {{10}^{ - 5}}\,/{\,^ \circ }C} \right]$

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.

Calculate radiation power for sphere whose temperature is $227^{\circ} \mathrm{C}$ and radius $0.2$ and emissivity $0.8.$

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

A body cools down from $50^{\circ} \mathrm{C}$ to $45^{\circ} \mathrm{C}$ in $5 \mathrm{~min}$ and $45^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$ is $8 \mathrm{~min}$. Find the temperature of the surrounding. Assume Newton's law of cooling is valid.

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

If the temperature of radiating body increased by $50 \%$. The percentage increase in radiation energy is closest to

Statement-I: Invar steel is used to prepare clock pendulum.
Statement-II: The coefficient of linear expansion of invar steel is infinity.

The coefficient of cubical expansion of water is negative between

A pendulum clock having copper rod keeps correct time at $20^{\circ} \mathrm{C}$. It gains 15 seconds per day if cooled to $0^{\circ} \mathrm{C}$. The coefficient of linear expansion of copper is

A solid ball of metal has a concentric spherical cavity within it. If the ball is heated, the volume of the cavity will

The coefficient of volume expansion of an ideal gas at constant pressure and at temperature $T$. K is equal to

An iron sphere has a radius of $10 \mathrm{~cm}$ at a temperature of $0^{\circ} \mathrm{C}$. Calculate the change in the volume of the sphere, if it is heated to $100^{\circ} \mathrm{C}$. Coefficient of linear expansion of iron $=11 \times 10^{-6}{ }^{\circ} \mathrm{C}^{-1}$.

A faulty thermometer reads the melting point and boiling point of water as $-1^{\circ} \mathrm{C}$ and $104^{\circ} \mathrm{C}$ respectively. The temperature of the object is measured as $40^{\circ} \mathrm{C}$ using that thermometer. The true temperature of the object is: