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A copper rod $2 m$ long has a circular cross-section of radius $1 cm .$ One end is kept at $100 ° C$ and the other at $0 ° C$ and the surface is covered by non- conducting material to check the heat losses through the surface. The thermal resistance of the $bar$ in degree Kelvin per watt (closest to nearest integer) is (Take thermal conductivity $K = 401 W m^{- 1} K^{- 1}$ of copper)

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Important Questions on Heat and Thermodynamics

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Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Three rods of identical cross-sectional area and made from the same metal, form the sides of an isosceles triangle

A B C

right angled at

B

as shown in figure. The point

A

and

B

are maintained at temperature

T

and

\sqrt{2} T

respectively, in the steady state. Now, assuming that only heat conduction takes place. The temperature of point

C

will be

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Two materials having coefficients of thermal conductivity

3 K

and

K

and thickness

d

and

3 d

respectively, are joined to form a slab as shown in the figure. The temperatures of the outer surfaces are

θ_{2}

and

θ_{1}

respectively,

(θ_{2} > θ_{1})

. The temperature at the interface is
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HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Consider a pair of insulating blocks with thermal resistances $R_{1}$ , and $R_{2}$ as shown in the figure. The temperature $θ$ at the boundary between the two blocks is

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HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

In steady state heat conduction, the equations that determine the heat current

j (r)

[heat flowing per unit time per unit area] and temperature

T (r)

in space are exactly the same as those governing the electric field

E (r)

and electrostatic potential

V (r)

with the equivalence given in the table below.

Heat flow	Electrostatics
$T (r)$	$V (r)$
$j (r)$	$E (r)$

We exploit this equivalence to predict the rate

Q

of total heat flowing by conduction from the surfaces of spheres of varying radii, all maintained at the same temperature. If

Q \propto R^{n},

where

R

is the radius, then the value of

n

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

A metallic prong consists of $4$ rods made of the same material, cross-section, and same lengths as shown.

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The three forked ends are kept at $100^{o} C$ and the handle end is at $0^{o} C .$ The temperature of the junction is

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Statement $A :$ Convection involves flow of matter within a fluid due to unequal temperatures of its parts.

Statement $B :$ A hot bar placed under a running tap water loses heat due to effect of convection within water.

Statement. $C :$ Heat transfer always involves temperature difference between two systems.

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Three rods of identical cross-section and length are made of three different materials of thermal conductivity $K_{1}, K_{2}$ and $K_{3}$ , respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod is maintained at $100 ° C$ and the other at $0 ° C$ (see figure). If the joints of the rod are at $70 ° C$ and $20 ° C$ in steady and there is no loss of energy from the surface of the rod, the correct relationship between $K_{1}, K_{2}$ and $K_{3}$ is :

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EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Two identical metal wires of thermal conductivities

K_{1}

and

K_{2}

respectively are connected in series. The effective thermal conductivity of the combination is:

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Two rods A and B of different materials are welded together as shown in figure. Their thermal conductivities are $K_{1}$ and $K_{2}$ . The thermal conductivity of the composite rod will be

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HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Three rods of Copper, Brass and Steel are welded together to form a Y-shaped structure. Area of cross-section of each rod is

4 {cm}^{2}

. End of copper rod is maintained at

100 ° C

. Where as ends of brass and steel are kept at

0 ° C

. Lengths of the copper, brass and steel rods are

46, 13

and

12 cms

respectively. The rods are thermally insulated from surroundings except at ends. Thermal conductivities of copper, brass and steel are

0.92, 0.26

and

0.12

CGS units respectively. Rate of heat flow through copper rod is :

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

The freezer in a refrigerator is located at the top section so that

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

The two ends of a metal rod are maintained at temperatures

100 ° C

and

110 ° C

. The rate of heat flow in the rod is found to be

4.0 J s^{- 1}

. If the ends are maintained at temperatures

200 ° C

and

210 ° C

, the rate of heat flow will be:

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Prevost's theory of heat exchange is not applicable at temperature

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Consider a ball of mass $100 g$ attached to one end of a spring $(k = 800 N m^{- 1})$ and immersed in $0.5 kg$ water. Assume the complete system is in thermal equilibrium. The spring is now stretched to $20 cm$ and the mass is released so that it vibrates up and down. Estimate the change in temperature of water before the vibrations stop.

(Specific heat of the material of the ball $= 400 J {kg}^{- 1} K^{- 1}$ and Specific heat of water $= 4200 J {kg}^{- 1} K^{- 1}$ )

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

The temperature $θ$ at the junction of two insulating sheets, having thermal resistances $R_{1}$ and $R_{2}$ as well as top and bottom temperatures $θ_{1}$ and $θ_{2}$ (as shown in figure) is given by :

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MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

A rod $C D$ of thermal resistance $10 K W^{- 1}$ is joined at the middle of an identical rod $A B$ as shown in figure. The ends $A, B$ and $D$ are maintained at $200 ° C, 100 ° C$ and $125 ° C$ respectively. The heat current in $C D$ is $P W$ . The value of $P$ is

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MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

A uniform copper rod of

50 cm

length is insulated on the sides and has its ends exposed to ice and steam respectively. If there is a layer of water

1 mm

thick at each end, the temperature gradient

(in ° C m^{- 1})

in the bar is (assume that the thermal conductivity of copper is

400 W m^{- 1} K^{- 1}

and water is

0 .4 W m^{- 1} K^{- 1}

)

EASY

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

The unit of thermal conductivity is

MEDIUM

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

Solar energy is incident normally on the earth's surface at the rate of about

1 .4 kW m^{- 2}

. The distance between the earth and the sun is

1 .5 \times 10^{11} m

. Energy

(E)

and mass

(m)

are related by the Einstein equation,

E = m c^{2}

where

c = (3 \times 10^{8} m s^{- 1})

is the speed of light in free space. The decrease in the mass of the sun is

HARD

Physics>Heat and Thermodynamics>Heat and Thermodynamics>Thermal Conductivity

A thin piece of thermal conductor of constant thermal conductivity insulated on the lateral sides connects two reservoirs which are maintained at temperatures, $T_{1}$ and, $T_{2}$ as shown. Assuming that the system is in steady-state, which of the following plots best represents the dependence of the rate of change of entropy on the ratio of temperatures, $\frac{T_{1}}{T_{2}}$

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Important Questions on Heat and Thermodynamics

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