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Six identical rods are joined together to form a network as shown. A temperature difference of $Δ T$ can be maintained between two points. Considering heat flow through conduction only, in steady state :-

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Important Questions on Thermal Properties of Matter

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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

EASY

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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:

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

In a steady state, the temperature at the end

A

and end

B

of a

20 cm

long rod

A B

are

100 ° C

and

0 ° C

. The temperature of a point,

9 cm

from

A

EASY

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

A heat source at

T = 10^{3} K

is connected to another heat reservoir at

T = 10^{2} K

by a copper slab which is

1 m

thick. Given that the thermal conductivity of copper is

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

, the energy flux through it in the steady-state is:

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

Two thin metallic spherical shells of radii

r_{1}

and

r_{2} (r_{1} < r_{2})

are placed with their centres coinciding. A material of thermal conductivity

K

is filled in the space between the shells. The inner shell is maintained at temperature

θ_{1}

and the outer shell at temperature

θ_{2} (θ_{1} < θ_{2}) .

The rate at which heat flows radially through the material is :

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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

EASY

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

The phenomenon of emission of electron from hot bodies is called

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Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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
Question Image

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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 :

Question Image

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

Two rods whose lengths are

l_{1}

and

l_{2}

with heat conductivity co-efficients

k_{1}

and

k_{2}

are placed end to end. The heat conductivity coefficient of a uniform rod of length

l_{1} + l_{2}

whose conductivity is same as that of the system of these two rods is

EASY

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

Which of the following is NOT a reversible process?

MEDIUM

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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

Question Image

EASY

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

A piece of metal and a piece of wood are kept at a temperature of $45 ° C$ .

On touching the two with hand,

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

An ice cube of dimensions

60 cm \times 50 cm \times 20 cm

is placed in an insulation box of wall thickness

1 cm

. The box keeping the ice cube at

0 ° C

of temperature is brought to a room of temperature

40 ° C

. The rate of melting of ice is approximately: (Latent heat of fusion of ice is

3.4 \times 10^{5} J {kg}^{- 1}

and thermal conduction of insulation wall is

0.05 W m^{- 1} ° C^{- 1}

)

EASY

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

Two metallic blocks $M_{1}$ and $M_{2}$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of $M_{2}$ is $K$ then the thermal conductivity of $M_{1}$ will be : [Assume steady state heat conduction]

Question Image

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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

Question Image

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

Two rectangular blocks, having identical dimensions, can be arranged either in configuration

I

or in configuration

I I

as shown in the figure. One of the blocks has thermal conductivity

K

and the other

2 K

. The temperature difference between the ends along the x-axis is the same in both the configurations. It takes

9 s

to transport a certain amount of heat from the hot end to cold end in the configuration

I

. The time to transport the same amount of heat in the configuration

II

HARD

Physics>Thermal Physics>Thermal Properties of Matter>Heat Conduction in One Dimension

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, $\frac{T_{1}}{T_{2}}$

Question Image

Six identical rods are joined together to form a network as shown. A temperature difference of ΔT can be maintained between two points. Considering heat flow through conduction only, in steady state :-

Important Questions on Thermal Properties of Matter

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Six identical rods are joined together to form a network as shown. A temperature difference of $Δ T$ can be maintained between two points. Considering heat flow through conduction only, in steady state :-