Arihant AIEEE Physics

D.B. Singh

Chapter 18

Heat Transfer - all with Video Answers

Educators

Chapter Questions

Problem 1

If the wavelength of maximum intensity of radiation emitted by sun and moon are $0.5 \times 10^{-6} \mathrm{~m}$ and $10^{-4} \mathrm{~m}$ respectively, the ratio of their temperatures is:
(a) $\frac{1}{100}$
(b) $\frac{1}{200}$
(c) 100
(d) 200

Ajay Singhal

Ajay Singhal

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Problem 2

A red glass piece is heated until it glows in dark. The colour of the glow will be:
(a) red
(b) orange
(c) green
(d) violet

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Numerade Educator

Problem 3

An object is at temperature of $400^{\circ} \mathrm{C}$. At what temperature would it radiate energy twice as fast ? The temperature of the surrounding may be assumed to be negligible :
(a) $200^{\circ} \mathrm{C}$
(b) $200 \mathrm{~K}$
(c) $800^{\circ} \mathrm{C}$
(d) $800 \mathrm{~K}$

Ajay Singhal

Numerade Educator

Problem 4

The maximum wavelength of radiation emitted at $200 \mathrm{~K}$ is $4 \mu \mathrm{m}$ what will be the maximum wavelength of radiation emitted at $2400 \mathrm{~K}$ ?
(a) $3.33 \mu \mathrm{m}$
(b) $0.66 \mu \mathrm{m}$
(c) $1 \mu \mathrm{m}$
(d) $1 \mathrm{~m}$

Ajay Singhal

Numerade Educator

Problem 5

For the measurement of temperature of the order of $400^{\circ} \mathrm{C}$, the preferred thermometer will be :
(a) Hg thermometer
(b) alcohol thermometer
(c) radiation thermometer
(d) thermocouple

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Problem 6

For measuring temperature near absolute zero the thermometer used is:
(a) thermoelectric thermometer
(b) radiation thermometer
(c) magnetic thermometer
(d) resistance thermometer

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Problem 7

The mode of transfer of heat which requires no medium, is called as :
(a) radiation
(b) conduction
(c) combusion
(d) convection

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Problem 8

If $K$ and $\sigma$ respectively are the thermal and electrical conductivities of a metal at absolute temperature $T$ then :(a) $\frac{K}{\sigma T}=$ constant
(b) $\frac{K}{\sigma}=$ constant
(c) $\frac{K}{T}=$ constant
(d) $\frac{\sigma}{K T}=$ constant

Ajay Singhal

Numerade Educator

Problem 9

The thermal conductivity of copper is:
(a) less than that of iron
(b) less than that of aluminium
(c) less than that of wood
(d) more than that of all the three given above

Ajay Singhal

Numerade Educator

Problem 10

Though air is bad conductor yet a body kept in air losses heat quickly this is due to :
(a) conduction
(b) convection
(c) radiation
(d) none of these

Ajay Singhal

Numerade Educator

Problem 11

A bucket full of hot water is kept in a room and it cools from $75^{\circ} \mathrm{C}$ to $70^{\circ} \mathrm{C}$ in $T_{1}$ minutes, from $70^{\circ} \mathrm{C}$ to $65^{\circ} \mathrm{C}$ in $T_{2}$ minutes and from $65^{\circ} \mathrm{C}$ to $60^{\circ} \mathrm{C}$ in $T_{3}$ minutes then :
(a) $T_{1}=T_{2}=T_{3}$
(b) $T_{1}<T_{2}<T_{3}$
(c) $T_{1}>T_{2}>T_{3}$
(d) $T_{1}<T_{2}>T_{3}$

Ajay Singhal

Numerade Educator

Problem 12

In a closed room, heat transfer takes place by:
(a) conduction
(b) convection
(c) radiation
(d) all of these

Ajay Singhal

Numerade Educator

Problem 13

A body of length $1 \mathrm{~m}$ having cross-sectional area $0.75 \mathrm{~m}^{2}$ has thermal conductivity $6000 \mathrm{~J} / \mathrm{s}$ then the temperature difference if $\mathrm{K}=200 \mathrm{Jm}^{-1} \mathrm{~K}^{-1}$, will be :
(a) $20^{\circ} \mathrm{C}$
(b) $40^{\circ} \mathrm{C}$
(c) $80^{\circ} \mathrm{C}$
(d) $100^{\circ} \mathrm{C}$

Ajay Singhal

Numerade Educator

Problem 14

The volume of block of metal changes by $0.12 \%$ when heated through $20^{\circ} \mathrm{C}$ then $\alpha$ is :
(a) $2.0 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}$
(b) $4.0 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}$
(c) $6.0 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}$
(d) $8.0 \times 10^{-5}\left({ }^{\circ} \mathrm{C}\right)^{-1}$

Ajay Singhal

Numerade Educator

Problem 15

$1 \mathrm{~g}$ of ice at $0^{\circ} \mathrm{C}$ is mixed with $1 \mathrm{~g}$ of steam at $100^{\circ} \mathrm{C}$. After thermal equilibrium is attained, the temperature of mixture will be :
(a) $1^{\circ} \mathrm{C}$
(b) $50^{\circ} \mathrm{C}$
(c) $81^{\circ} \mathrm{C}$
(d) $100^{\circ} \mathrm{C}$

Ajay Singhal

Numerade Educator

Problem 16

Woollen clothes keep the body warm because wool :
(a) is a bad conductor
(b) increases the temperature of the body
(c) decreases the temperature of the body
(d) all of the above

Ajay Singhal

Numerade Educator

Problem 17

In a composite rod, when two rods of different lengths and of the same area of cross-section, are joined end to end then if $K$ is the effective coefficient of thermal conductivity $\frac{l_{1}+l_{2}}{K}$ is equal to :
(a) $\frac{l_{1}}{K_{1}}-\frac{l_{2}}{K_{2}}$
(b) $\frac{l_{1}}{K_{2}}=\frac{l_{2}}{K_{1}}$
(c) $\frac{l_{1}}{K_{1}}+\frac{l_{2}}{K_{2}}$
(d) $\frac{l_{1}}{K_{2}}+\frac{l_{2}}{K_{1}}$

Ajay Singhal

Numerade Educator

Problem 18

An aluminium rod of length $L$ and cross- sectional area $2 A^{\prime}$ is joined with a copper rod of length $2 L^{\prime}$ and area of cross-section is $' A^{\prime}$, as shown in figure. The temperature of aluminium-copper junction in the steady state of the system is:

Dheeraj Sharma

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Problem 19

A uniform metal ring with centre $C$ have two points $A$ and $B$, such that angle $A C B$ is $\theta . A$ and $B$ are maintainedat two different constant temperatures. If the angle between $A$ and $B$, i.e. $\theta=180^{\circ}$, the rate of heat flow from $A$ to $B$ is $1.2 \mathrm{~W}$, then what will be the rate, when $\theta=90^{\circ}$ ?
(a) $0.6 \mathrm{~W}$
(b) $0.9 \mathrm{~W}$
(c) $1.6 \mathrm{~W}$
(d) $1.8 \mathrm{~W}$

Dheeraj Sharma

Numerade Educator

Problem 20

Two rods $A$ and $B$ of same length and cross-sectional area are connected in parallel and a temperature difference of $100^{\circ} \mathrm{C}$ is maintained across the combination as shown in the figure. If the thermal conductivity of the $\operatorname{rod} A$ is $3 K$ and that of $\operatorname{rod} B$ is $K$, then what is the equivalent thermal resistance?(a) $R=\frac{1}{4 K A}$
(b) $R=\frac{1}{2 K A}$
(c) $R=\frac{2 l}{K A}$
(d) $R=\frac{3 l}{2 K A}$

Ajay Singhal

Numerade Educator

Problem 21

A metallic sphere having inner and outer radii $a$ and $b$ respectively has thermal con- ductivity
$$
K=\frac{K_{C}}{r} \quad(a<r<b)
$$
The thermal resistance between inner surface and outer surface is:
(a) $\frac{(b-a)}{4 \pi K_{0}}$
(b) $\frac{\left(b^{2}-a^{2}\right)}{4 \pi K_{0} a b}$
(c) $\frac{4 \pi K_{0}}{(b-a)}$
(d) none of these

Dheeraj Sharma

Numerade Educator

Problem 22

In above problem if the temperature of inner and outer surfaces are $\theta_{1}^{\circ}$ and $\theta_{2}^{\circ} \mathrm{C}\left(\theta_{1}>\theta_{2}\right) .$ The rate of flow of heat in steady state is:
(a) $\frac{4 \pi K_{0}\left(\theta_{1}-\theta_{2}\right)}{(b-a)}$
(b) $\frac{4 \pi K_{0}(b-a)}{\left(\theta_{1}-\theta_{2}\right)}$
(c) $\frac{4 \pi K_{0} a b\left(\theta_{1}-\theta_{2}\right)}{\left(b^{2}-a^{2}\right)}$
(d) none of these

Dheeraj Sharma

Numerade Educator

Problem 23

Five wires each of crosssectional area $A$ and length $l$ are combined as shown in figure. The thermal conductivity
$A$ and $C$ is :
$K_{1}$ and $K_{2}$ respectively. The equivalent thermal of copper and steel are
resistance between points
(a) $\frac{l}{\left(K_{1}+K_{2}\right) A}$
(b) $\frac{2 l}{\left(K_{1}+K_{2}\right) A}$
(c) $\frac{l\left(K_{1}+K_{2}\right)}{K_{1} K_{2} A}$
(d) none of these

Dheeraj Sharma

Numerade Educator

Problem 24

In previous problem if $A$ is maintained at $100^{\circ} \mathrm{C}$ and $C$ is maintained at $0^{\circ} \mathrm{C}$. The rate emitted at $C$ is : (assume the curve surfaces of rods are thermally insulated)
(a) $\frac{50 A\left(K_{1}+K_{2}\right)}{l}$
(b) $\frac{100 A\left(K_{1}+K_{2}\right)}{l}$
(c) $\frac{A\left(K_{1}+K_{2}\right)}{l}$
(d) none of these

Ajay Singhal

Numerade Educator

Problem 25

Three rods are arranged as a letter $Y$. The rods have same dimensions and have thermal conductivities $3 K, 2 K$ and $K$. If the ends of the rods are at a temperature of $100^{\circ} \mathrm{C}$, $50^{\circ} \mathrm{C}$ and $0^{\circ} \mathrm{C}$, then temperature of the junction $O$ is :(a) $75^{\circ} \mathrm{C}$
(b) $\frac{200^{\circ} \mathrm{C}}{3}$
(c) $40^{\circ} \mathrm{C}$
(d) $\frac{100^{\circ} \mathrm{C}}{3}$

Ajay Singhal

Numerade Educator

Problem 26

A metal rod of length $L$ and cross-sectional area $A$ converts a large tank of water at temperature $\theta_{0}$ and a small vessel containing mass $m$ of water at initial temperature of $\theta_{1}\left(<\theta_{0}\right)$. If the thermal conductivity of rod is $K$, then the time taken for the temperature of water in smaller vessel to become $\theta_{2}\left(\theta_{1}<\theta_{2}<\theta_{0}\right)$ is :
(Given: Specific heat capacity of water is $s$ and all other heat capacities are neglected)
(ì) $\bar{i}=\frac{m s}{K A} \operatorname{iog} \frac{\left(\theta_{0}-\theta_{1}\right)}{\left(\theta_{0}-\theta_{2}\right)}$
(b) $T=\frac{L m s}{K A} \log \left(\frac{\theta_{0}-\theta_{1}}{\theta_{0}-\theta_{2}}\right)$
(c) $T=\frac{2 m L s}{K A}\left(\log \frac{\left(\theta_{0}-\theta_{1}\right)}{\theta_{0}-\theta_{2}}\right)$
(d) none of the above

Dheeraj Sharma

Numerade Educator

Problem 27

The thermal conductivity of a material of a cylinder of radius $R$ is $K_{1}$, which is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2 R$ made of the material of thermal conductivity $K_{2}$. The two ends of the combined system are maintained at two different temperatures. Assume, that 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:
(a) $K_{1}+K_{2}$
(b) $\frac{K_{1} K_{2}}{\left(K_{1}+K_{2}\right)}$
(c) $\frac{\left(K_{1}+3 K_{2}\right)}{4}$
(d) $\frac{\left(3 K_{1}+K_{2}\right)}{4}$

Dheeraj Sharma

Numerade Educator

Problem 28

Choose the correct option, if heat is flowing through a conductor of length $l$ from $x=0$ to $x=l$. Assume thermal resistance per unit length is uniform :

Dheeraj Sharma

Numerade Educator

Problem 29

If the thermal conductivity of the material of the rod of length $l$, is $K$, then the rate of heat flow through a tapering rod, tapering from radius $r_{1}$ and $r_{2}$, if the temperature of the ends are maintained at $T_{1}$ and $T_{2}$, is:
(a) $\frac{\pi K r_{1} r_{2}\left(T_{1}+T_{2}\right)}{l}$
(b) $\frac{\pi K r_{1} r_{2}\left(T_{1}-T_{2}\right)}{l}$
(c) $\frac{\pi K r_{1} r_{2}\left(T_{1}-T_{2}\right)}{2 l}$
(d) $\frac{\pi K r_{1}^{2}\left(T_{1}-T_{2}\right)}{l}$

Dheeraj Sharma

Numerade Educator

Problem 30

The time in which a layer of ice of thickness $h$ will grow on the surface of the pond of surface area $A$, when the surrounding temperature falls to $-T^{\circ} \mathrm{C}$ is :
(Assume $K=$ thermal conductivity of ice, $\rho=$ density fo water, $L=$ latent heat of fusion)
(a) $t=\frac{p L}{2 K T} h^{2}$
(b) $t=\frac{\rho L}{K T} h^{2}$
(c) $t:=\frac{\rho L h^{2}}{3 K T}$
(d) $t=\frac{\rho L h^{2}}{4 K T}$

Dheeraj Sharma

Numerade Educator

Problem 31

Which process has maximum rate of heat transfer?
(a) Conduction
(b) Convection
(c) Radiation
(d) In all the above heat is transferred with the same velocity.

Ajay Singhal

Numerade Educator

Problem 32

The propagation of heat in air takes place by:
(a) conduction
(b) convection
(c) radiation
(d) all of these

Ajay Singhal

Numerade Educator

Problem 33

The propagation of heat in vacuum takes place by:
(a) conduction
(b) convection
(c) radiation
(d) none of these

Ajay Singhal

Numerade Educator

Problem 34

The thermal radiation emitted by a body per second per unit area is $\frac{\Delta H}{A \Delta t}=k T^{4}$. If $\sigma$ is Stefan's constant, then body :
(a) may be polished
(b) may be black body
(c) must be black body
(d) must not be black body

Saman Zulfiqar

Numerade Educator

Problem 35

Read the following statements carefully
(A) Black body radiation is white
(B) Emissivity of a body is equal to its absorptive power Mark correct option:
(a) Statement (A) is correct

Saman Zulfiqar

Numerade Educator

Problem 36

The power ${ }^{\prime} P^{\prime}$ is received by a surface at temperature $T_{0} K$ from a small sphere at temperature $T\left(T>>T_{0}\right)$ and at a distance ' $d^{\prime}$. If both ' $T^{\prime}$ and ' $d^{\prime}$ are doubled, then power received by surface will become:
(a) $P$
(b) $2 P$
(c) $4 P$
(d) $16 P$

Saman Zulfiqar

Numerade Educator

Problem 37

What will be the increment in heat energy radiated when the temperature of hot body is raised by $5 \%$ ?
(a) $5 \%$
(b) $6 \%$
(c) $11.65 \%$
(d) $21.55 \%$

Saman Zulfiqar

Numerade Educator

Problem 38

Two spheres of the same material have radii $r$ and $4 r$ and temperatures $2 T_{0}$ and $T_{0}$ respectively. The ratio of rate of radiation of energy by the spheres is:
(a) $1: 1$
(b) $1: 2$
(c) $2: 1$
(d) $3: 1$

Saman Zulfiqar

Numerade Educator

Problem 39

A sphere, a cube and a thin circular plate all of same material having same mass are initially heated to $200^{\circ} \mathrm{C}$. Which of these will cool fastest?
(a) Circular plate
(b) Sphere
(c) Cube
(d) All of these

Saman Zulfiqar

Numerade Educator

Problem 40

A sphere and a cube of the same material and same total surface area are placed in the same evacuated space turn by turn, after they are heated to the same temperature. Let initial rate of cooling of sphere and cube are $R_{1}$ and $R_{2}$, respectively, then compare their initial rate of cooling:
(a) $R_{1}>R_{2}$
(b) $R_{1}<R_{2}$
(c) $R_{1}=R_{2}$
(d) none of these

Saman Zulfiqar

Numerade Educator

Problem 41

A body at a temperature of $727^{\circ} \mathrm{C}$ and has surface area $5 \mathrm{~cm}^{2}$, radiates $300 \mathrm{~J}$ of energy each minute. The emissivity is :
(Given: Boltzmann constant $=5.67 \times 10^{-8}$ watt $\mathrm{m}^{2}(\mathrm{~K})^{4}$ )
(a) $e=0.18$
(b) $e=0.02$
(c) $e=0.2$
(d) $e=0.15$

Saman Zulfiqar

Numerade Educator

Problem 42

Choose the correct relation, when the temperature of an isolated black body falls from $T_{1}$ to $T_{2}$ in time ' $t$ ', and assume ' $c^{\prime}$ to be a constant :
(a) $t-c\left(\frac{1}{T_{2}}-\frac{1}{T_{1}}\right)$
(b) $t=c\left(\frac{1}{T_{2}^{2}}-\frac{1}{T_{1}^{2}}\right)$
(c) $t=c\left(\frac{1}{T_{2}^{3}} \ldots \frac{1}{T_{1}{ }^{3}}\right)$
(d) $t=c\left(\frac{1}{T_{2}{ }^{4}}-\frac{1}{T_{1}{ }^{4}}\right)$

Saman Zulfiqar

Numerade Educator

Problem 43

The temperature and the surface area of the body are $227^{\circ} \mathrm{C}$ and $0.15 \mathrm{~m}^{2}$ respectively. If its transmitting power is negligible and reflecting power is $0.5$, then the thermal power of the body is:
(Given: $\left.\sigma=5.67 \times 10^{-8} \mathrm{~J} / \mathrm{m}^{2} \mathrm{~s} \mathrm{~K}\right)$
(a) 300 watt
(b) $265.78$ watt
(c) 201 watt
(d) $320.89$ watt

Saman Zulfiqar

Numerade Educator

Problem 44

The surface temperature of the sun is ' $T$ K and the solar constant for a plate is ' $s$ '. The sun subtends an angle $\theta$ at the planet. Then:(a) $s \propto T^{i}$
(b) $s \propto T^{2}$
(c) $s \propto \theta^{2}$
(d) $s \propto \theta$

Saman Zulfiqar

Numerade Educator

Problem 45

Newton's law of cooling is derived from
(a) Wien's displacement law
(b) Kirchhoff's law of radiation
(c) Stefan's law
(d) Planck's law

Saman Zulfiqar

Numerade Educator

Problem 46

Read the following statements
(A) Water can be boiled inside the artificial satellite by convection.
(B) Heavy liquid can be boiled in artificial satellite by convection. Mark correct option/s:
(a) Both statements are correct
(b) Both statements are wrong
(c) $\mathrm{A}$ is correct but $\mathrm{B}$ is wrong
(d) $B$ is correct but $A$ is wrong

Ajay Singhal

Numerade Educator

Problem 47

Read the following statements
(A) Water can be boiled inside the artificial satellite by convection.
(B) Heavy liquid can be boiled in artificial satellite by convection. Mark correct option/s:
(a) Both statements are correct
(b) Both statements are wrong
(c) $\mathrm{A}$ is correct but $\mathrm{B}$ is wrong
(d) $B$ is correct but $A$ is wrong

Vysakh M

Numerade Educator

Problem 48

The cooling curve of pure wax material after heating is shown in the figure. It first cools from $A$ to $B$ and solidifies along $B D$. The ratio of $L / C$, if $L$ and $C$ are respective values of specific latent heat of fusion and specific heat capacity of the liquid wax is : (Assume rate of heat loss remain constant)
(a) 40
(b) 80
(c) 100
(d) 20

Saman Zulfiqar

Numerade Educator

Problem 49

A metal block is heated well above the room temperature and then left to cool in the room. Choose the correct graph which shows the rate of cooling:

Saman Zulfiqar

Numerade Educator

Problem 50

A body initially at $60^{\circ} \mathrm{C}$ cools to $50^{\circ} \mathrm{C}$ in 10 minutes. What will be its temperature at the end of next 10 minutes, if the room temperature is $25^{\circ} \mathrm{C}$. Assume Newton's law of cooling :
(a) $42.85^{\circ} \mathrm{C}$
(b) $45^{\circ} \mathrm{C}$
(c) $40.46^{\circ} \mathrm{C}$
(d) $44.23^{\circ} \mathrm{C}$

Saman Zulfiqar

Numerade Educator

Problem 51

A body starts cooling in a surrounding which is at a temperature of $\theta_{0}-\mathrm{A}$ graph is between temperature and time $t$. Newton's cooling is Tangents are the curve at and $Q$ at temperatures of $\quad \theta_{2}$
respectively. If tangent meet the time axis at angle of $\phi_{2}$ and $\phi_{1}$, then :
(a) $\frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{1}-\theta_{0}}{\theta_{2}-\theta_{0}}$
(b) $\frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{2}-\theta_{0}}{\theta_{1}-\theta_{0}}$
(c) $\frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{1}}{\theta_{2}}$
(d) $\frac{\tan \phi_{2}}{\tan \phi_{1}}=\frac{\theta_{2}}{\theta_{1}}$

Saman Zulfiqar

Numerade Educator

Problem 52

When a blackened platinum wire is heated gradualiy, it appears?
(a) first blue, then red and finally white
(b) first red, then blue and finally white
(c) first white, then blue and finally red
(d) first red, then white and finally blue

Saman Zulfiqar

Numerade Educator

Problem 53

Surface temperature of the sun as estimated is $6032.25 \mathrm{~K}$. The wavelength at which sun radiates maximum energy, is: (Given: Wein's constant $=0.2898 \mathrm{~cm}-\mathrm{K}$
(a) $\lambda_{m}=5000 \AA$
(b) $\lambda_{m}=4804.2 \AA$
(c) $\lambda_{m}=3809.5 \AA$
(d) $\lambda_{m}=2891.6 \AA$

Saman Zulfiqar

Numerade Educator