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Modes of heat transfer - conduction - class-XI

Description: modes of heat transfer - conduction
Number of Questions: 82
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Tags: properties of bulk matter physics heat and thermodynamics temperature and heat thermal properties thermal properties of matter
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Ebonite handles are used to handle hot utensil because they are bad conductors of heat.

  1. True

  2. False


Correct Option: A
Explanation:

Yes, it's true that ebonite are bad conductors of heat so they are used to handle hot utensis.

Three rods of identical cross-sectional area and made from the same metal from the sides of an isosceles triangles ABC, right-angled at B. The point A and B are maintained at temperatures T and $(\sqrt{2})$T respectively. In the steady state, the temperature of the point C is $T _C$. Assuming that only heat conduction takes place, $T _C/T$ is?

  1. $\dfrac{1}{2\left(\sqrt{2}-1\right)}$

  2. $\dfrac{3}{\sqrt{2}+1}$

  3. $\dfrac{1}{\sqrt{3}\left(\sqrt{2}-1\right)}$

  4. $\dfrac{1}{\sqrt{2}+1}$


Correct Option: B

If two bodies A and B of $50^{0} C$ comes in contact with each other. The heat will flow 

  1. Body A $\rightarrow$ Body B

  2. Body B $\rightarrow$ Body A

  3. nowhere

  4. from both the bodies


Correct Option: C
Explanation:

Both the bodies are at same temperature, so there will be no transfer of heat from one body to other body.

If the pressure of a gas is doubled then its thermal conductivity will :

  1. remain constant

  2. decrease

  3. decrease exponentially

  4. increase


Correct Option: A
Explanation:

Thermal conductivity of a gas is independent of the pressure as compared to solid and liquid. So the thermal conductivity of gas will remain constant.

If $K$ denotes coefficient of thermal conductivity, $d$ the density and $C$ the specific heat, the unit of $X$, where $X = K/dc$, will be

  1. $cm\space sec$

  2. $cm^2\space sec^{-2}$

  3. $cm \space sec^{2}$

  4. $cm^2 \space sec^{-1}$


Correct Option: D
Explanation:

The Units of the respective quantities in SI are:

  • $[K] = J(mKs)^{-1}$
  • $[\rho] = kg(m)^{-3}$
  • $[c] = J(kgK)^{-1}$
$[X] = \dfrac{[K]}{[\rho] [c]} = \dfrac{J(mKs)^{-1}}{(kg(m)^{-3})(J(kgK)^{-1})}$
$[X] = m^{2}s^{-1}$ or in CGS $cm^{2}s^{-1}$

A body of length 1 m have an area of cross-section as 0.75 $m^{2}$. If rate of heat conduction of the body is 6000 J/s and coefficient of thermal conductivity is 200 $Jm^{-1}$ $K^{-1}$, then the temperature difference between the two ends of the body is

  1. $30^{\circ}C$

  2. $20^{\circ}C$

  3. $40^{\circ}C$

  4. $80^{\circ}C$


Correct Option: C

Two rods one hallow and the other solid made of the same material have the same length of $20 cm $ and radius of $2 cm$. When their temperature is increased through the same amount of $50^oC$, their expansion ratio $E _h:E _s$ will be:

  1. $1:8$

  2. $1:4$

  3. $1:1$

  4. $1:2$


Correct Option: A

Equal temperature difference exists between the ends of two metallic rods $1 $ and $2$ of length. Their thermal conductivities are $K _1$ and $K _2$ and cross sectional areas represents $A _1$ and $A _2$. The condition for equal rate of heat transfer is:

  1. $K _1A _2=K _2A _1$

  2. $K _1A _1=K _2A _2$

  3. $K _1A _1^2=K _2A _2^2$

  4. $K _1^2A _2=K _2^2A _1$


Correct Option: B
Explanation:
Equal temperature difference exists between the two metallic rods 1 and 2.
The heat transfer$=\dfrac{KA \Delta T}{l}$
For equal rate of heat transfer,
$\dfrac{K _1 A _1 \Delta T}{l}=\dfrac{K _2A _2 \Delta T}{l}$
$K _1A _1=K _2A _2$
The correct option is B.

Conduction of heat is possible:

  1. when the bodies are apart from each other

  2. when the bodies have same temperature and in thermal contact

  3. when they have different temperatures maintaining distance between them

  4. bodies should be in contact and should have different temperatures


Correct Option: D
Explanation:

Conduction is only possible when the bodies in contact have a temperature difference.

More energetic molecules of a body transfer some of their energy to other molecules, without any change in their position in:

  1. conduction

  2. convection

  3. radiation

  4. none of these


Correct Option: A
Explanation:

Conduction is defined as the process of transferring heat from molecule to molecule, without the actual movement of molecules.

Here, more energetic molecules of a body transfer some of their energy to other molecules, without any change in their position.

The thermal conductivity of the plate depends upon

  1. the temperature difference between the two sides

  2. the thickness of the plate

  3. the area of the plate

  4. nature of the material


Correct Option: D
Explanation:

Thermal conductivity of any object depends solely on the material of the object.
It is an intrinsic property and is independent on dimensions/mass/etc of the body.
For example, all iron rods will have same thermal conductivity.
All copper rods will have same thermal conductivity.
But, thermal conductivity of iron rod will be different from that of copper rod.

Which of the following qualities are best suited for handling a cooking utensil?

  1. high specific heat and low thermal conductivity

  2. high specific heat and high thermal conductivity

  3. low specific heat and low thermal conductivity

  4. low specific heat and high thermal conductivity


Correct Option: A
Explanation:

High specific heat means high energy required to increase temperature.
Hence for a given amount of energy, temperature would be less for high specific heat.
Low conductivity means heat is not conveyed to all portions of the conductor easily.
Hence, handling the instrument would be easy.

If pressure on a gas is increased from $P$ to $2P$, then its heat conductivity

  1. increases

  2. decreases

  3. becomes zero

  4. remains unchanged


Correct Option: D
Explanation:

Conductivity of gas does not depend on pressure.

Thermal conductivity of a metal rod depends on :

  1. area of cross section

  2. temperature gradient

  3. time of flow of heat

  4. none of these


Correct Option: D
Explanation:

Thermal conductivity is characteristic to the material and doesn't depend on any of the factors given.
In fact, heat flow depends on the factors given in options list.

Conduction is:

  1. the process of transfer of heat which does not require any material medium

  2. the process of transferring heat from molecule to molecule, without the actual movement of molecules

  3. the process in which molecules conduct heat by moving from hotter regions to colder regions

  4. the process in which heat energy moves through the medium of protons


Correct Option: B
Explanation:

Conduction is defined as the process of transferring heat from molecule to molecule, without the actual movement of molecules.

The coefficient of thermal conductivity of a metallic rod does not depend upon :

  1. the length of the rod

  2. the cross-sectional area of the rod

  3. the temperature difference between the ends of the rod

  4. the nature of the metal


Correct Option: A,B,C
Explanation:

Coefficient of $Thermal$ $Conductivity$ is the internal property of the metal and is independent of all the $external$ properties of the material.

So Coefficient of $Thermal$ $Conductivity$ is independent of dimensions, temperatures and other external factors too. It only depend on nature of material.

Conduction is ,

  1. the process of transfer of heat which does not require any material medium

  2. the process of transferring heat from molecule to molecule, with out any movement of molecules

  3. the process in which molecules conduct heat by moving from hotter regions to colder regions

  4. the process in which heat energy moves through the medium of protons


Correct Option: B
Explanation:

Conduction is the process by which heat or electricity is directly transmitted through the material of a substance without movement of the material.

It is warmer to have two thin blankets than to have single thick blanket because:

  1. Thick blankets cannot give more warmth

  2. Two blankets allow more heat to pass through them

  3. Air between the two blankets is a good conductor of heat

  4. Air between the thin blankets does not allow heat to pass through it since it is a bad conductor


Correct Option: D
Explanation:

Air is bad conductor of heat, so it does not allow the heat to pass through, while the single thick blanket is a better conductor of heat so it is less effective.

In which mode of transfer of heat molecules pass on heat energy to neighbouring molecules without actually moving from their positions?

  1. convection

  2. radiation

  3. conduction

  4. none of these


Correct Option: C
Explanation:
Conduction is the mode of heat transfer of heat molecules pass on heat energy to neighbouring molecules without actually moving from their positions.
Conduction is the transfer of heat from one substance to another by direct contact without mixing of masses.

In a steady state the temperature of the ends A and B of a 20 cm long rod AB is 100$^o$C and 0$^o$C. The temperature at the point c distant 9 cm from a is :

  1. $45^o$C

  2. $55^o$C

  3. $60^o$C

  4. $65^o$C


Correct Option: B
Explanation:
Temperature increasing per unit length $=\cfrac{100-0}{20}=5^oC/cm$
Temperature at $9cm$ from $a \\ =100^oC-(5^oC/cm\times 9cm) \\ =55^oC$

Sea and land breezes are caused because of :

  1. convection

  2. cyclones

  3. rains

  4. conduction


Correct Option: A
Explanation:

All wind is caused by a pressure gradient. In the case of land or sea breeze, the pressure gradient is due to the different heating and cooling rates of the area.

Lake or sea breeze and land breeze are on a comparatively small scale when viewing meteorological events. This is important to note because large scale heating and small scale heating work differently. In the case of small scale heating, the increase in heat causes an increase in volume which in turn lowers the pressure in that area.
In the morning the land heats up much faster than the water. This eventually results in a pressure gradient with a lower pressure on the land due to the quicker heating. Air moves from the water to the land in the form of a sea breeze.

After sunset, the land cools much quicker than the water. As a result, the volume of the air over the water is higher and the pressure decreases. Ar then moves over the water as a land breeze.

Conduction cannot take place in:

  1. Copper

  2. Iron

  3. Aluminium

  4. Vacuum


Correct Option: D
Explanation:

A solid medium is required for conduction to take place. Since, vaccum does not have a medium, conduction does not take place.

Transmission of heat by the movement of heated particles is called

  1. Conduction

  2. Convection

  3. Radiation

  4. Regelation

  5. Expansion


Correct Option: B
Explanation:

Convection is a mode of heat transfer where in the molecules near the heat source get heated up, they expand , becomes less dense , and rise upwards .whereas the relatively colder sink to the bottom and eventually get heated up. Thus transmission of heat by the movement of heated particles of heat particles is called convection.

The only liquid which is a good conductor of heat is-

  1. water

  2. turpentine

  3. alcohol

  4. mercury


Correct Option: D
Explanation:
The liquid which is good conductor of heat is mercury.
 Thermal conductivity is $8.30W/(mK)$ of mercury.

State whether given statement is True or False
Air conducts heat

  1. True

  2. False


Correct Option: B
Explanation:

False, air do not conducts heat.

But air is poor conductor of heat because its molecules are not in continuous contact with one another unlike a solid. Heat by conduction passes more quickly in solid because the molecules vibrations immediately affect the neighbours. Air molecules only transfer energy upon collision and the collision time is too small for significant energy transfer to occur. Heat transfer in air is mainly due to convection, which in general is less efficient than in conduction.

Give reason : Birds puff up their feathers in winter 

  1. so that they can trap more air

  2. so that can develop charge

  3. cant say

  4. so that friction reduces


Correct Option: A
Explanation:

Birds puff up their feathers in winter because by doing so they trap a large amount of air in their body which in turn acts as an insulator and does not allow the heat from their bodies to flow out

Using a heating blanket to get warm is an example of-

  1. Conduction

  2. Convection

  3. Radiation

  4. none of these


Correct Option: A
Explanation:
Using a heating blanket to get warm is example of conduction.
As conduction is the transfer of heat from one body to another by direct contact without mixing of masses. When we cover ourselves with blanket, there is direct contact. And blanket insulates the heat present in the body and does not out heat to escape and loose warmth.

Same quantity of ice is filled in each of the two metal containers P and Q having the same size, shape and wall thickness but made of different materials. The containers are kept in identical surroundings. The ice in P melts completely in time $t _1$ whereas that in Q takes a time $t _2$. The ratio of thermal conductivities of the materials of P and Q is

  1. $t _2 : t _1$

  2. $t _1 : t _2$

  3. $t _1^2 : t _2^2$

  4. $t _2^2 : t _1^2$


Correct Option: A
Explanation:

The power transported per unit area is given as

$\dfrac{\Delta Q}{A\Delta t}=-\kappa\dfrac{\Delta T}{\Delta x}$
Thus $\Delta Q=-\kappa \Delta tA\dfrac{\Delta T}{\Delta x}$
Same amount of heat was needed to melt ice in both P and Q. Hence 
$\kappa _{P}t _1=\kappa _Qt _2$
$\implies \dfrac{\kappa _P}{\kappa _Q}=\dfrac{t _2}{t _1}$

Two thermometers are used to record the temperature of a room. If the bulb of one is wrapped in wet hanky:

  1. The temperature recorded by both will be same.

  2. The temperature recorded by the wet-bulb thermometer will be greater than that recorded by the other.

  3. The temperature recorded by dry-bulb thermometer will be greater than that recorded by the other

  4. None of the above


Correct Option: C
Explanation:

The thermometer whose bulb is wrapped by wet hanky; undergoes evaporation process; and we know that evaporation results in cooling, so the wet bulb, thermometer will record less temperature than that of dry bulb thermometer.

Two plates of same thickness form a composite plate. The temperature on one side of the plate is $0^0 C$. If the ratio of thermal conductivities is 3 : 1 and the plate with higher thermal conductivity has one of its faces at $0^0 C$, then the temperature of the interface is 

  1. $45^0 C$

  2. $40^0 C$

  3. $20^0 C$

  4. $15^0 C$


Correct Option: D

A body P is connected to a large body Q through a conducting rod of length. I crossectional  area. A and thermal conductivity K. This assembly is placed in an an atmosplere of temperature ${ T } _{ A }$ and body Q is also maintained at temperature ${ T } _{ A }$. Let beat capacity of body P is C and it is unitally at temperature ${ T } _{ 1 }$. If in time t second temperature of body P falls to ${ T } _{ 2 }$. Then chose the correct option .

  1. $log\left[ \dfrac { { T } _{ 2 }-{ T } _{ A } }{ { T } _{ 1 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } \right] t$

  2. $log\left[ \dfrac { { T } _{ 2 }-{ T } _{ A } }{ { T } _{ 12 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } \right] t$

  3. $log\left[ \dfrac { { T } _{ 1 }-{ T } _{ A } }{ { T } _{ 2 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } .t \right]$

  4. $log\left[ \dfrac { { T } _{ 1 }-{ T } _{ A } }{ { T } _{ 2 }-{ T } _{ A } } \right] =\left[ { K } _{ 1 }\dfrac { KA }{ LC } \right] t$


Correct Option: C

The dimensions of coefficient of thermal conductivity is:

  1. $M \ L^{.2} T^{.2} K^{.1}$

  2. $M \ L \ T^{.-3} K^{.-1}$

  3. $M \ L \ T^{.2} K^{.1}$

  4. $M \ L \ T^{.3} K$


Correct Option: B
Explanation:

The dimension of coefficient of thermal conductivity is ${M^1}{L^1}{T^{ - 3}}{K^{ - 1}}$ 

Hence,
option $B$ is correct answer.

A wall has two layers A and B, each made of different material. Both the layers have the same thickness. The thermal conductivity of the material of A is twice that of B. Under thermal equilibrium, the temperature difference across the wall is $36^o$C. The temperature difference across the layer A is?

  1. $6^o$C

  2. $12^o$C

  3. $18^o$C

  4. $24^o$C


Correct Option: B

a wall has two layers $A$ and $B,$ each made of  a different material.Both the layers have the same thickness.The thermal conductivity of the material of $A$ is twice that of $B.$ Under thermal equilibrium, the temperature difference across the wall is ${36^ \circ }C$ The temperature difference across the layer $A$ is  

  1. ${6^ \circ }C$

  2. ${12^ \circ }C$

  3. ${18^ \circ }C$

  4. ${24^ \circ }C$


Correct Option: C

An aluminium meter rod of area of cross section $4cm^2$ with K=0.5 cal $g^{-1}$ $^oC^{-1}$ is observed that at steady state 360 cal of heat flows per minute.
The temperature gradient along the rod is

  1. $3^oC/cm$

  2. $6^oC/cm$

  3. $12^oC/cm$

  4. $20^oC/cm$


Correct Option: A

A conducting ring lies fixed on a horizontal plane. If a charged nonmagnetic particle is released from a point (on the axis) at some height from the plane, then :

  1. an induced current will flow in clockwise or anticlockwise direction in the loop depending upon the nature of the charge

  2. the acceleration of the particle will decrease as it comes down

  3. the rate of production of heat in the ring will increase as the particle comes down

  4. no heat will be produced in the ring


Correct Option: D

Ratio of radius of curvature of cylindrical emitters of same type is $1:4$ and their temp. are in ration $2:1$. Then ration of amount of heat emitted by them is-(For Cylinder length = radius);-

  1. 2:1

  2. 1:1

  3. 4:1

  4. 1:4


Correct Option: B

If the coefficient of conductivity of aluminium is $0.5cal/cm-sec-^oC,$ then in order to conduct $10cal/sec-cm^2$ in the steady state, the temperature gradient in aluminium must be

  1. $5^oC/cm$

  2. $10^oC/cm$

  3. $20^oC/cm$

  4. $10.5^oC/cm$


Correct Option: C

a rod of length 1 m having cross-sectional area 0.75 $m^{2}$ conduts heat at 6000 $Js^{-1}$. Then the temperature difference across the rod is, if k=200 $Wm^{-1}$ $K^{-1}$

  1. $20^{\circ}C$

  2. $40^{\circ}C$

  3. $80^{\circ}C$

  4. $1000^{\circ}C$


Correct Option: B

A sphere, a cube and a thin circular plate all made of same substance and all have same mass. These are heated to $200^{o}C$ and then placed in a room. Then the:-

  1. Temperature of sphere drops to room temperature at last.

  2. Temperature of cube drops to room temperature at last.

  3. Temperature of thin circular plate drops to room temperature at last.

  4. Temperature of all the three drops to room temperature at the same time


Correct Option: A

The dimensional formula for coefficient of thermal conductivity is:

  1. $[MLTK]$

  2. $[MLT{K^{ - 1}}]$

  3. $[MLT^{-1}{K^{ - 1}}]$

  4. $[ML{T^{ - 3}}{k^{ - 1}}]$


Correct Option: D
Explanation:

The for the coefficient of thermal conductivity is

$K _{th}=\dfrac{Q\Delta x}{A\Delta T t}$
Dimensional formula of $K _{th}$
$[K _{th}]=\dfrac{[Heat].[length]}{[Area].[Temperature].[time]}$
$[K _{th}]=\dfrac{[ML^2T^{-2}].[L]}{[L^2].[K].[T]}$
$[K _{th}]=[MLT^{-3}K^{-1}]$

The correct option is D.

Conduction is not possible in

  1. iron

  2. water

  3. vacuum

  4. aluminium


Correct Option: C

A spherical black body of radius $(R)$ when heated to certain temperature and left in vaccum. cools at a rate $'x' $ Now a caity of radius $(R/2)$ is made concentrically from this sphere. The rate of cooling of the remaining sphere will be.....................

  1. $\cfrac { x }{ 8 } $

  2. $\cfrac { 7x }{ 8 } $

  3. $\cfrac { 8x }{ 8 } $

  4. $\cfrac { x }{ 7 } $


Correct Option: A

A hollow copper sphere and a hollow copper cube, of same surface area and negligible thickness, are filled with warm water of same temperature and placed in an enclosure of constant temperature, a few degrees below that of the bodies. Then in the beginning:

  1. the rate of energy lost by the sphere is greater than that by the cube

  2. the rate of fall of temperature for sphere is greater than that for the cube.

  3. the rate of energy lost by the sphere is less than that by the cube

  4. the rate of fall of temperature for sphere is less than that for the cube.


Correct Option: B

A spherical body of radius n. If its rate of cooling is R, then

  1. $R \propto \frac{1}{n}$

  2. $R \propto \frac{1}{n^2}$

  3. $R \propto n$

  4. $R \propto n^2$


Correct Option: C

A copper block of mass $500gm$ and $Sp.$ Heat $0.1 cal/gm/^{o}{C}$ is heated from ${30}^{o}C$ to ${40}^{o}C$. Another identical copper block $B$ of same mass is heated from ${35}^{o}C$ to ${40}^{o}C$. The ratio of their thermal capacities is 

  1. $1:2$

  2. $2:1$

  3. $1:1$

  4. $1:4$


Correct Option: C

Heat required to convert one gram of ice at $0^{ _-^0}C$ into steam at $100^{ _-^0}C$ is (given $L _{steam}$ = 536 cal/gm)-

  1. 100 calorie

  2. 0.01 kilocalorie

  3. 716 calorie

  4. 1 kilocaorie


Correct Option: C

Air is filled at $60^o$C in a vessel of open mouth. The vessel is heated at temperature T so that $\dfrac{1}{4}$ th part of air escapes. Assuming volume of container remaining constant, find value of T. 

  1. $80^oC$

  2. $444^oC$

  3. $333^oC$

  4. $171^oC$


Correct Option: D

Cooking utensils are made up of 

  1. Good conductors of heat

  2. bad conductors of heat

  3. neither good conduction not bad conductors of heat

  4. None of these


Correct Option: A

$1\ kcal $ per hour of heat flowing through a rod of iron. When the rod is cut down to $4$ pieces then what will be the heat flowing through each piece having same differential temperature?

  1. $1 / 2\ \mathrm { kcal }$

  2. $1 / 4\ \mathrm { kcal }$

  3. $1\ \mathrm { kcal }$

  4. $1 / 15\ \mathrm { kcal }$.


Correct Option: A

A metal rod of length $2m$ has cross sectional area $2A$ and as shown in figure$.$ The ends are maintained at temperature $100^0C$ and $70^0C$.$ The tem[temperature at middle point C is

  1. $90^0C$

  2. $30^0C$

  3. $45^0C$

  4. $60^0C$


Correct Option: A
Explanation:

$\begin{array}{l} Let\, \, q\, \, be\, \, temperatrure\, \, middle\, \, po{ { int } }\, \, C\, and\, \, in\, \, series\, \, rate\, \, of\, \, heat\, \, flow\, \, is\, \, same \ K\left( { 2A } \right) \left( { 100-\theta  } \right) =KA\left( { \theta -70 } \right)  \ 200-2\theta =\theta -70 \ 3\theta =270 \ \theta ={ 90^{ 0 } }C \end{array}$

Hence,
option $(A)$ is correct answer.

The thermal conductivity of a rod depends on :

  1. length

  2. mass

  3. area of cross-section

  4. material of rod


Correct Option: D
Explanation:

Thermal conductivity is a material property.
It does not depend on area of cross section, length and mass of the rod.
option (D) is the correct answer.

The heat capacity of a metal is 4200 J/k. Its water equivalent is-

  1. $0.5 kg$

  2. $1 kg$

  3. $1.5 k$

  4. $2 kg$


Correct Option: A

A steel drill is making 180 revolutions per minute under a constant couple of 5 Nm. If it drills a hole in 7 seconds in a steel block of mass 600 gm, the rise in temperature of the block is: (S=0.I cal/gm/K)

  1. $46 ^ { 0 } C$

  2. $1.3 ^ { 0 } C$

  3. $5.2 ^ { 0 } C$

  4. $3 ^ { 0 } C$


Correct Option: C

Three copper blocks of masses ${ M } _{ 1 },{ M } _{ 2 }$ and ${ M } _{ 3 }$ kg respectively are brought into thermal contact till they reach equilibrium. Before contact. they were at ${ T } _{ 1 },{ T } _{ 2 },{ T } _{ 3 }$ $\left( { T } _{ 1 }>{ T } _{ 2 }>{ T } _{ 3 } \right) .$ Assuming there is no heat loss to the surrounding, the equilibrium temperature T (s is specitc heat of copper)

  1. $T=\dfrac { { T } _{ 1 }+{ T } _{ 2 }+{ T } _{ 3 } }{ 3 } $

  2. $T=\dfrac { { M } _{ 1 }{ T } _{ 1 }+{ M } _{ 2 }{ T } _{ 2 }+{ M } _{ 3 }{ T } _{ 3 } }{ { M } _{ 1 }+{ M } _{ 2 }+{ M } _{ 3 } } $

  3. $T=\dfrac { { M } _{ 1 }{ T } _{ 1 }+{ M } _{ 2 }{ T } _{ 2 }+{ M } _{ 3 }{ T } _{ 3 } }{ 3{ (M } _{ 1 }+{ M } _{ 2 }+{ M } _{ 3 }) } $

  4. $T=\dfrac { { M } _{ 1 }{ T } _{ 1 }s+{ M } _{ 2 }{ T } _{ 2 }s+{ M } _{ 3 }{ T } _{ 3 }s }{ { M } _{ 1 }+{ M } _{ 2 }+{ M } _{ 3 } } $


Correct Option: C

Two walls of thickness   $d _ { 1 }$   and   $d _ { 2 }$   thermal conductivities  $K _ { 1 }$  and  $K _ { 2 }$  are in contact. In the steady state if the temperatures at the outer surfaces are  $T _ { 1 }$  and  $T _ { 2 },$  the temperature at the common wall will be

  1. $\dfrac { K _ { 1 } T _ { 1 } + K _ { 2 } T _ { 2 } } { d _ { 1 } + d _ { 2 } }$

  2. $\dfrac { K _{ { 1 } }T _{ 1 }d _{ { 2 } }+K _{ { 2 } }T _{ { 2 } }d _{ { 1 } } }{ K _{ { 1 } }d _{ { 2 } }+K _{ { 2 } }d _{ { 1 } } } $

  3. $\dfrac { \left( K _ { 1 } d _ { 1 } + K _ { 2 } d _ { 2 } \right) T _ { 1 } T _ { 2 } } { T _ { 1 } + T _ { 2 } }$

  4. $\dfrac { K _{ { 1 } }d _{ { 1 } }T _{ 1 }+K _{ { 2 } }d _{ { 2 } }T _{ { 2 } } }{ K _{ { 1 } }d _{ { 1 } }+K _{ { 2 } }d _{ { 2 } } } $


Correct Option: B
Explanation:

$\begin{array}{l} Under\, steady\, state\, heat\, flux\, per\, unit\, area\, k\left( { \frac { { dT } }{ { dx } }  } \right)  \ is\, same\, across\, two\, walls.\, hence,\, we\, have \ { K _{ 1 } }\dfrac { { { T _{ 1 } }-{ T _{ c } } } }{ { { d _{ 1 } } } } ={ K _{ 2 } }\dfrac { { { T _{ c } }-{ T _{ 2 } } } }{ { { d _{ 2 } } } }  \ where\, { T _{ c } }\, is\, common\, wall\, temperature.\, \, solving\, for\, { T _{ c } }\, we\, will\, get \ { T _{ c } }=\dfrac { { { T _{ 1 } }+\alpha { T _{ 2 } } } }{ { \alpha +1 } }  \ Where\, \alpha =\dfrac { { { d _{ 1 } } } }{ { { d _{ 2 } } } } \, \dfrac { { { k _{ 2 } } } }{ { { k _{ 2 } } } }  \end{array}$

$\begin{array}{l} On\, putting\, the\, value\, of\, \alpha =\dfrac { { { d _{ 1 } } } }{ { { d _{ 2 } } } } .\dfrac { { { k _{ 1 } } } }{ { { k _{ 2 } } } }  \ Then,\, { T _{ c } }=\dfrac { { { k _{ 1 } }{ T _{ 1 } }{ d _{ 2 } }+{ k _{ 2 } }{ T _{ 2 } }{ d _{ 1 } } } }{ { { k _{ 1 } }{ d _{ 2 } }+{ k _{ 2 } }{ d _{ 1 } } } }  \end{array}$
Hence,Option $B$ is the correct answer.

Two rods of length  $\mathrm { d _ { 1 } } ,$  and  $\mathrm { d _ { 2 } } ,$  and coefficient of thermal conductivities  $\mathrm { K } _ { 1 }$  and  $\mathrm { K } _ { 2 }$  are kept touching each other. Both have the same area of cross-section. The equivalent of thermal conductivity is

  1. $K _ { 1 } + K _ { 2 }$

  2. $\mathrm { K } _ { 1 } \mathrm { d } _ { 1 } + \mathrm { K } _ { 2 } \mathrm { d } _ { 2 }$

  3. $\dfrac { \mathrm { d } _ { 1 } \mathrm { K } _ { 2 } + \mathrm { d } _ { 2 } \mathrm { K } _ { 2 } } { \mathrm { d } _ { 1 } + \mathrm { d } _ { 2 } }$

  4. $\dfrac { d _ { 1 } + d _ { 2 } } { \left( d _ { 1 } K _ { 2 } \right) + \left( d _ { 2 } K _ { 2 } \right) }$


Correct Option: D

Three roads identical area of cross-section and made from the same metal from the sides of an isosceles triangle ABC, right angled at B. The points A and B are maintained at temperature  T and $ \sqrt {2} T $ respectively. IN the steady state the temperature that only point C is $ T _c $ Assuming that only conduction takes place $ \frac {T _c}{T} is $

  1. $ \frac { 1 }{ \left( \sqrt { 2 } +1 \right) } $

  2. $ \frac { 1 }{ \left( \sqrt { 2 } -1 \right) } $

  3. $ \frac { 1 }{ 2\left( \sqrt { 2 } +1 \right) } $

  4. $ \frac { 1 }{ \sqrt { 3 } \left( \sqrt { 2 } -1 \right) } $


Correct Option: A

Two rods of equal length and area of cross-sectional are kept parallel and lagged between temperature $ 20^o C and 80^oC $ The ration of the effective thermal conductivity to that of the first rod is
 $ \left[ the\quad ration\left( \frac { K _ 1 }{ K _ 2 }  \right) =\frac { 3 }{ 4 }  \right]  $

  1. 7 : 4

  2. 7 : 6

  3. 4 : 7

  4. 7 : 8


Correct Option: A

In engines water is used as coolant, because

  1. It good conductor of heat energy.

  2. It has low density.

  3. It has LOW specific heat.

  4. It's bad conductor of heat energy.


Correct Option: D

Fix a lighted candle on a table. Put a glass chimney over the candle in such a way that air can enter the chimney from below. What happens to the flame? 

  1. Continues burning

  2. Flickers off

  3. Flickers off and give smoke

  4. None of these


Correct Option: C

Two spheres of different materials one with double the radius and one - fourth wall thickness of the other, are filled with $r$ ice. If the time taken for complete melting ice in the large radius one is $25 minutes$ and that for smaller one is $16 minutes$, $r$ the ratio of thermal conductivity of the materials of larger sphere to the smaller sphere is $r$

  1. $4:5$

  2. $5:4$

  3. $25:1$

  4. $1:25$


Correct Option: D

At a common temperature ,a block of wood and a block of metal feel equally cool or hot. The temperatures of metal and wood are

  1. $Less$ $than$ $the$ $temperature$ $of$ $the$ $body$

  2. $Equal$ $than$ $the$ $temperature$ $of$ $the$ $body$

  3. $Greater$ $than$ $the$ $temperature$ $of$ $the$ $body$

  4. $Either$ $(a)$ $or$ $(c)$


Correct Option: B

Choose the correct experiment to demonstrate the transfer of heat by the process of conduction.

  1. Take two metal blocks of same size & shape and heat one of them to a considerable temperature, then allow both the blocks to touch each other, after a while, you will see the other block gets heated due to contact.

  2. Take two metal blocks of same size & shape and heat one of them to a considerable temperature, then keep the blocks separate, after a while you will see the other block gets heated due to contact.

  3. Take two metal blocks of same size & shape and heat one of them to a considerable temperature, then allow both the blocks to touch each other after the block get cooled down, after a while you will see the other block gets heated due to contact.

  4. None of above


Correct Option: A
Explanation:
Take two metal blocks of same size & shape and heat one of them to a considerable temperature, then allow both the blocks to touch each other, after a while you will see the other block gets heated due to contact.

If a rod is in a variable state (not in steady state), then

  1. Temperature gradient remains constant

  2. Temperature of rod is function of time and distance from one of end

  3. Temperature of rod is only function of distance from one of end

  4. Temperature of rod is only function of time


Correct Option: B

State true or false:
The more is the temperature difference of hot and cold body more slowly the heat flows from it into the cold body

  1. True

  2. False


Correct Option: B
Explanation:
The amount of heat leaving the hot object will be equal to the amount of heat received by the colder object (assuming nothing else is around to receive some of the heat). The rate at which heat transfers from the hotter object to the colder object increases with the temperature difference between the objects.

By which of the following methods could a cup of hot tea lose heat when placed on metallic table in a class room
a) conduction
b) convection
c) radiation
d) evaporation of liquid.

  1. a, b

  2. b,c

  3. a,b,c

  4. a,b,c,d


Correct Option: C
Explanation:

Conduction occurs through the walls of the cup.
Radiation occurs from the top surface.
Convection occurs at the top of the cup.
Evaporation of liquid also occurs.

The quantity of heat flowing for $10 \ s$ through a rod of length $40\ cm$, area $50 \ cm^{2}$ is $200\ J$. If the temperature difference at the ends of the rod is 80$^{o}$C , the coefficient of thermal conductivity of the rod in Wm$^{-1}$K$^{-1}$ is:

  1. $20$

  2. $60$

  3. $80$

  4. $120$


Correct Option: A
Explanation:

$Q = 200$
$A = 50 \times 10^{-4}\ m^2$
${\theta}^{} _{1} = 80^\circ C    ;   \ \ {\theta}^{} _{2} = 0$
$t = 10\ s ; \ \    l  = 0.40\ m$
$Q = \dfrac{KA\Delta T t}{L}$
$200 = \dfrac{K  \times 50\times 10^{-4}\times    80\times    10}{0.4}$ 
$K = 20\ W/mK$ 

SI units of thermal conductivity are

  1. W/m - K.

  2. W/m

  3. W/K

  4. None


Correct Option: A
Explanation:

From the formula:

Rate of heat flow $= \dfrac{(k \times A \times (Change\ of\ temp))}{Thickness}$
Units of $k$ are $W/m-K$.

The thermal conductivity of a rod depends on

  1. length

  2. mas

  3. area of cross section

  4. material of the rod


Correct Option: D

Coefficient of thermal conductivity :

  1. depends upon nature of the material of the body

  2. is independent of dimensions of the body

  3. both 1 and 2

  4. only 1


Correct Option: A
Explanation:

Coefficient of thermal conductivity of a rod is an intrinsic property. It depends on the material of the rod and not on the dimensions of the rod.

A red hot brick is placed on an iron tripod stand which stands on a large block of copper. The brick loses heat by:

  1. conduction

  2. conduction and radiation

  3. conduction and convection

  4. conduction, convection, and radiation


Correct Option: B
Explanation:

The brick loses heat (i) by conduction through iron tripod stand to the copper block which is then radiated away and convection currents are set up in the surrounding air, and (ii) by radiation.

A constant voltage is applied between the two ends of a uniform metallic wire. Some heat is
developed in it. The heat developed is doubled if

  1. both the length and the radius of the wire are halved.

  2. both the length and the radius of the wire are doubled

  3. the radius of the wire is doubled

  4. the length of the wire is doubled


Correct Option: B

In the Arctic region hemispherical houses called Igloos are made of ice. It is possible to maintain a temperature inside an Igloo as high as $20^o$C because.

  1. Ice has high thermal conductivity

  2. Ice has low thermal conductivity

  3. Ice has high specific heat

  4. Ice has higher density than water


Correct Option: B
Explanation:

ice is good at trapping heat. It is a  good insulator and low thermal conductivity .

A long silver tea spoon is placed in a cup filled with hot tea. After some time, the exposed end (the end which is not dipped in tea) of the spoon becomes hot even without a direct contact with the tea. This phenomenon can be explained mainly by_______

  1. conduction

  2. reflection

  3. radiation

  4. thermal expansion


Correct Option: A
Explanation:

As atoms in the spoon vibrates about their equilibrium positions and transfer energy form one end to other end. This process is called conduction.

A piece of metal is heated to increase its temperature from $5^{\circ}C$ to $15^{\circ}C$. The increase in temperature expressed in $K$ and $^{\circ}F$ are respectively.

  1. $10\ K, 18^{\circ}F$

  2. $283\ K, 50^{\circ}F$

  3. $18\ K, 10^{\circ}F$

  4. $50\ K, 283^{\circ}F$


Correct Option: A
Explanation:

$K=273.16+C\F=\cfrac{9C}{5}+32\quad dK=dC \quad dF=\cfrac{9}{5}dC$

A/Q, $dC=15-5=10\ \therefore dK=10K,\quad dF=\cfrac{9}{5}\times10=18°F$

A slab of stone area $3500{cm}^{2}$ and thickness $10cm$ is exposed on the lower surface to steam at ${100}^{o}C$. A block of ice at ${0}^{o}C$ rests on upper surface of the slab. In one hour $4.8kg$ of ice of melted. The thermal conductivity of the stone is $J{s}^{-1}$ ${m}^{-1}$ ${k} _{-1}$ is
(Latent heat of ice $=3.36\times { 10 }^{5 }J/kg$)

  1. $12.0$

  2. $10.5$

  3. $1.02$

  4. $1.24$


Correct Option: D
Explanation:

Given :  $A = 3500 \ cm^2 = 0.35 \ m^2$         $l = 10 \ cm = 0.1 \ m$             $\Delta T =100-0 = 100^o C$
Mass of ice melted  $m = 4.8 \ kg$
Time taken  $t = 1 \ hr = 3600 \ s$
Latent heat of ice  $L = 3.36\times 10^{5} \ J/kg$
Heat absorbed by ice = Heat conducted by slab
$\therefore$   $mL = \dfrac{KA t\Delta T}{l}$
Or    $4.8\times 3.36\times 10^{5} = \dfrac{K(0.35) (3600)(100)}{0.1}$
$\implies \ K = 1.24 \ Js^{-1} m^{-2} k^{-1}$

Which of the following minimizes the transference of heat in a thermos flask?
$1$. Conduction
$2$. Convection
$3$. Radiation

  1. $2$ and $3$

  2. $1$ and $2$

  3. $1, 2$ and $3$

  4. $1$ and $3$


Correct Option: C

The number of quanta of radiation of frequency $4.98 \times {10^{14}}{s^{ - 1}}$ required to melt 100 g of ice are (latent heat of melting of ice is 33 joule per g):

  1. ${10^{20}}$

  2. ${10^{22}}$

  3. ${10^{24}}$

  4. $6.023 \times {10^{21}}$


Correct Option: B
Explanation:

$1g$ requires $33J$. So, $100g$ will require $3300J$ heat.

Total quanta, 
E=hv
$=6.62\times { 10 }^{ -34 }\times 4.98\times { 10 }^{ 14 }\ =32.97\times { 10 }^{ -20 }$
$100g$ of ice will require=$\dfrac { 3300 }{ 32.97\times { 10 }^{ -20 } } =100.09$
$100$quantal=${ 10 }^{ 22 }J$

Two rods of the same length and diameter having thermal conductivities ${K _1}\,{K _2}$ are joined in parallel. The equivalent thermal conductivity of the combination is:

  1. $\dfrac{{{K _1}{K _2}}}{{{K _1} + {K _2}}}$

  2. ${{K _1} + {K _2}}$

  3. $\dfrac{{{K _1} + {K _2}}}{2}$

  4. $\sqrt {{K _1}{K _2}} $


Correct Option: A
Explanation:

$\dfrac{1}{{{K _{eq}}}} = \dfrac{1}{{{K _1}}} + \dfrac{1}{{{K _2}}}$

$\boxed{{K _{eq}} = \dfrac{{{K _1}{K _2}}}{{{K _1} + {K _2}}}}$

A cylinder of radius $R$ made of a material of thermal conductivity $K _1$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2R$ made of a material of thermal conductivity $K _2$. The two ends of the combined system are maintained at two different temperatures. There is no loss of heat across the cylindrical surface and the system is in steady state. The effective thermal conductivity of the system is?

  1. $K _1+K _2$

  2. $\dfrac{K _{1}+3K _{2}}{4}$

  3. $\dfrac{K _{1}+8K _{2}}{9}$

  4. $\dfrac{8K _{1}+K _{2}}{9}$


Correct Option: A,C

In order that the heat flows one part of a solid to another part, what is required ?

  1. uniform density

  2. temperature gradient

  3. density gradient

  4. uniform temperature


Correct Option: B
Explanation:

As heat flows from higher temperature to lower temperature, so a temperature gradient is required.

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