EASY

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The following figure shows three different arrangements of materials 1,2, and 3 to form a wall. Thermal conductivities are $k_{1} > k_{2} > k_{3}$ . The left side of the wall is $20 ° C$ higher than the right side. Temperature difference $∆ T$ across the material 1 has following relation in three cases

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Important Questions on Thermal Properties of Matter

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

Three rods of same dimensions have thermal conductivities $3 K, 2 K$ and $K$ . They are arranged as shown in the figure below. Then in the steady state the temperature of the junction $' P'$ is

Question Image

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

The unit of thermal conductivity is

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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>Thermal Properties of Matter>Heat Transfer

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>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

Which of the following is NOT a reversible process?

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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:

HARD

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

Cloudy nights are usually warmer than clear ones, because clouds

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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

EASY

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

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:

MEDIUM

Physics>Heat and Thermodynamics>Thermal Properties of Matter>Heat Transfer

Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures

T_{1} = 300 K a n d T_{2} = 100 K

as shown in the figure. The radius of the bigger cylinder is twice that of the smaller one and the thermal conductivities of the materials of the smaller and the larger cylinders are

K_{1} a n d K_{2}

, respectively. If the temperature at the junction of the two cylinders in the steady state is

200 K

, then

K_{1} / K_{2}

The following figure shows three different arrangements of materials 1,2, and 3 to form a wall. Thermal conductivities are k1>k2>k3. The left side of the wall is 20°C higher than the right side. Temperature difference ∆T across the material 1 has following relation in three cases

Important Questions on Thermal Properties of Matter

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