Thermal properties of matter practice · Mixed difficulty

Calculate the force required to prevent a steel wire of $1 \mathrm{~mm}^2$ cross-section from contracting when it cools from $60^{\circ} \mathrm{C}$ to $15^{\circ} \mathrm{C}$, if Young's modulus for steel is $2 \times 10^{11} \mathrm{~Nm}^{-2}$ and its coefficient of linear expansion is $0.000011^{\circ} \mathrm{C}^{-1}$.

A spherical ball of surface area $20 \mathrm{~cm}^2$ absorbs any radiation that falls on it. It is suspended in a closed box maintained at $57^{\circ} \mathrm{C}$. (a) Find the amount of radiation falling on the ball per second. (b) Find the net rate of heat flow to or from the ball at an instant when its temperature is $200^{\circ} \mathrm{C}$. Stefan constant $=6.0 \times 10^{-8}$ $\mathrm{W} \mathrm{m}{ }^{-2} \mathrm{~K}^{-4}$.

Assertion(A): Good conductors of electricity are also good conductors of heat.

Reason(R): In good conductors of electricity, there are large numbers of free electrons.

Which of the following statements are true
(a) Rubber contracts on heating
(b) Water expands on freezing
(c) Water contracts on heating from $0^{\circ} \mathrm{C}$ to $4^{\circ} \mathrm{C}$
(d) Water expands on heating from $4^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$

Heat is flowing through a rod of length $25.0 \mathrm{~cm}$ having cross-sectional area $8.80 \mathrm{~cm}^2$. The coefficient of thermal conductivity for the material of the rod is $K=9.2 \times 10^{-2} \mathrm{~kcal} \mathrm{~s}^{-1} \mathrm{~m}^{-1}{ }^{\circ} \mathrm{C}^{-1}$. The temperatures of the ends of the rod are $125^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$ in the steady state. Calculate temperature of a point at a distance of $10.0 \mathrm{~cm}$ from the hot end.

In a surrounding medium of temperature $10^{\circ} \mathrm{C}$, a body takes $7 \mathrm{~min}$ for a fall of temperature from $60^{\circ} \mathrm{C}$ to $40^{\circ} \mathrm{C}$. In what time the temperature of the body will fall from $40^{\circ} \mathrm{C}$ to $28^{\circ} \mathrm{C}$ ?

During constant temperature, we feel colder on a day when the relative humidity will be

A vertical glass jar is filled with water at $10^{\circ} {C}$. It has one thermometer at the top and another at the bottom. The central region of the jar is gradually cooled. It is found that the bottom thermometer reads $4^{\circ} {C}$ earlier than the top thermometer. And the top thermometer reads $0^{\circ} {C}$ earlier than the bottom thermometer. This is because

(A): A hollow metallic closed container maintained at a uniform temperature can act as a source of black body radiation.
(R): All metals acts as a black body

A metal rod of cross sectional area $1.0 \mathrm{~cm}^2$ is being heated at one end. At one time, the temperature gradient is $5.0^{\circ} \mathrm{C} \mathrm{cm}^{-1}$ at cross section $A$ and is $2.5^{\circ} \mathrm{Ccm}^{-1}$ at cross section $B$. Calculate the rate at which the temperature is increasing in the part $A B$ of the rod. The heat capacity of the part $A B=0.40 \mathrm{~J}^{\circ} \mathrm{C}^{-1}$, thermal conductivity of the material of the $\operatorname{rod}=200 \mathrm{~W} \mathrm{~m}^{-1}{}^\circ \mathrm{C}^{-1}$. Neglect any loss of heat to the atmosphere.

(A): In change of state from solid to liquid the temperature decreases until the entire amount of the solid substance melts.
(R): The phenomenon of refreezing is called melting.

The pressure of the gas in a constant volume gas thermometer at steam point $(373.15 \mathrm{~K})$ is $1.50 \times 10^4 \mathrm{~Pa}$. What will be the pressure at the triple point of water?

Wien’s displacement law for emission of radiation can be written as

$250 \mathrm{~gm}$ of water and equal volume of alcohol of mass $200 \mathrm{~gm}$ are replaced successively in the same calorimeter and cool from $60^{\circ} \mathrm{C}$ to $55^{\circ} \mathrm{C}$ in 130 seconds and 67 seconds respectively. If the water equivalent of the calorimeter is $10 \mathrm{~gm}$, then the specific heat of alcohol (in $\mathrm{cal} / \mathrm{gm}-{ }^{\circ} \mathrm{C}$) is

A metallic solid sphere has a cavity inside it. If this sphere is heated, then size of cavity will

Take a test rube nearly filled with water and put in the bottom a piece of paraffin wax, round which a piece of thick copper wire has been wound so that wax remains at the bottom. Temperature required for melting wax is $52^\circ \mathrm{C}$.
Statement-1: Heat the water at top where it will be seen to boil vigorously without melting wax.
Statement-2: Convection currents are not set-up when water column is heated from top and water is poor conductor of heat.

Statement A: A body of low thermal capacity gets heated or cooled quickly.
Statement B: Good emitters are bad reflectors.

$20 \mathrm{gm}$ water is at $10^{\circ} \mathrm{C}$ and $30 \mathrm{gm}$ water is at $40^{\circ} \mathrm{C}$ if these are mix together then find out the $\mathrm{T}_{\text {mix }}$

Assertion (A): When a Bimetallic strip made up of brass and iron is heated then brass lies on the convex side.
Reason (R): Due to lower value of coefficient of linear expansion, brass acquires convex shape.

As compared to the person with white skin, the person with black skin will experience

Two liquids $A$ and $B$ are at $30^\circ C\,\,\mathrm{and}\,\,20^\circ C$ respectively. When they are mixed in equal masses the temperature of the mixture is found to be $26^\circ C.$ The ratio of specific heats is

Wien's displacement law tells us that an extremely hot star looks

A faulty thermometer has its lower fixed point marked as $-10^{\circ} \mathrm{C}$ and upper fixed point marked as $110^{\circ}.$ At what temperature in celsius scale reading of both will be same:

Suppose you want to cool 200g of lemon water (Specific heat $4200\,{\text{J}}\,{\text{k}}{{\text{g}}^{ - 1}}{{\text{K}}^{ - 1}})$ at $30^\circ C$ by adding ice at $- 10^\circ C.$ The amount of ice that should be added, so that the final temperature becomes $0^\circ C$ with all ice melt is
(Specific heat of ice = $2000\,{\text{J}}\,{\text{k}}{{\text{g}}^{ - 1}}{{\text{K}}^{ - 1}})$

The freezing point a thermometer is marked as $20^\circ$ and the boiling point as $150^\circ .$ A temperature of $60^\circ C$ on this thermometer will be read as

The maximum wavelength in the energy distribution spectrum of sun is $4753\,\,\mathop {\text{A}}\limits^ \circ$ and its temperature is $6050 \mathrm{~K}$. The temperature of star whose energy distribution shows a maximum at $9506\,\,\mathop {\text{A}}\limits^ \circ$ is

Two spheres A and B have the same radii but the heat capacity of A is greater than that of B. The surfaces of both are painted black. They are heated to the same temperature and allowed to cool in vacuum. Then :

Statement A: Black body radiation is white
Statement B: Emissive power of a body is proportional to its absorptive power

The luminosity of the Rigel star is 17000 times that of the sun. Assume both to be perfectly black bodies. If the surface temperature of the sun is 6000 K, then the temperature of the star is

The surface of a lake is at ${1^ \circ }C$. Find the temperature of the bottom of the lake