Heat Transfer

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JEE Main 2019

A heat source at $T = 1 0^{3}$ K is connected to another heat reservoir at $T = 1 0^{2}$ K by a copper slab which is 1 m thick. Given that the thermal conductivity of copper is $0.1 WK^{- 1} m^{- 1}$ , the energy flux through it in the steady state is

90 Wm^{- 2}

(B)

65 Wm^{- 2}

(C)

120 Wm^{- 2}

(D)

200 Wm^{- 2}

LEVELJEE Advanced

The figure shows a system of two concentric spheres of radii $r_{1}$ and $r_{2}$ and kept at temperatures $T_{1}$ and $T_{2}$ , respectively. The radial rate of flow of heat in a substance between the two concentric spheres, is proportional to

(A)

\frac{( r _{2} - r _{1} )}{( r _{1} r _{2} )}

(B)

ln (\frac{r _{2}}{r _{1}})

(C)

\frac{r _{1} r _{2}}{( r _{2} - r _{1} )}

(D)

(r_{2} - r_{1})

JEE Main 2004

LEVELJEE Main

If the temperature of the sun were to increase from $T$ to $2 T$ and its radius from $R$ to $2 R$ , then the ratio of the radiant energy received on earth to what it was previously, will be

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

(A)

\frac{4 π K r _{1} r _{2} ( θ _{2} - θ _{1} )}{r _{2} - r _{1}}

(B)

\frac{π r _{1} r _{2} ( θ _{2} - θ _{1} )}{r _{2} - r _{1}}

(C)

\frac{K ( θ _{2} - θ _{1} )}{r _{2} - r _{1}}

(D)

\frac{K ( θ _{2} - θ _{1} ) ( r _{2} - r _{1} )}{4 π r _{1} r _{2}}

JEE Main 2006

LEVELJEE Main

Assuming the sun to be a spherical body of radius $R$ at a temperature of $T$ K, evaluate the total radiant power, incident on earth, at a distance $r$ from the sun. where, $r_{0}$ is the radius of the earth and $σ$ is Stefan's constant.

(A)

\frac{4 π r _{0}^{2} R ^{2} σ T ^{4}}{r ^{2}}

(B)

\frac{π r _{0}^{2} R ^{2} σ T ^{4}}{r ^{2}}

(C)

\frac{r _{0}^{2} R ^{2} σ T ^{4}}{4 π r ^{2}}

(D)

\frac{R ^{2} σ T ^{4}}{r ^{2}}

JEE Main 2014

LEVELJEE Main

Three rods of copper, brass and steel are welded together to form a Y-shaped structure. Area of cross-section of each rod = $4 cm^{2}$ . End of copper rod is maintained at $10 0^{\circ} C$ whereas ends of brass and steel are kept at $0^{\circ} C$ . Lengths of the copper, brass and steel rods are 46, 13 and 12 cm, respectively. The rods are thermally insulated from surrounding 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

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

(A)

\frac{θ _{2} R _{2} - θ _{1} R _{1}}{R _{2} - R _{1}}

(B)

\frac{θ _{1} R _{2} - θ _{2} R _{1}}{R _{2} - R _{1}}

(C)

\frac{θ _{1} R _{2} + θ _{2} R _{1}}{R _{1} + R _{2}}

(D)

\frac{θ _{1} R _{1} + θ _{2} R _{2}}{R _{1} + R _{2}}

JEE Main 2021

LEVELJEE Main

A rod $C D$ of thermal resistance $10.0 kW^{- 1}$ is joined at the middle of an identical rod $A B$ as shown in figure. The end $A, B$ and $D$ are maintained at $20 0^{\circ} C, 10 0^{\circ} C$ and $12 5^{\circ} C$ respectively. The heat current in $C D$ is $P$ watt. The value of $P$ is ....... .

JEE Main 2019

LEVELJEE Main

A cylinder of radius $R$ is surrounded by a cylindrical shell of inner radius $R$ and outer radius $2 R$ . The thermal conductivity of the material of the inner cylinder is $K_{1}$ and that of the outer cylinder is $K_{2}$ . Assuming no loss of heat, the effective thermal conductivity of the system for heat flowing along the length of the cylinder is

(A)

\frac{K _{1} + K _{2}}{2}

(B)

\frac{K _{1} + 3 K _{2}}{4}

(C)

\frac{2 K _{1} + 3 K _{2}}{5}

(D)

K_{1} + K_{2}

LEVELBoard

According to Newton's law of cooling, the rate of cooling of a body is proportional to $(Δ θ)^{n}$ , where $Δ θ$ is the difference of the temperature of the body and the surroundings, then $n$ is equal to

The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity $K$ and $2 K$ and thickness $x$ and $4 x$ respectively are $T_{2}$ and $T_{1}$ ( $T_{2} > T_{1}$ ). The rate of heat transfer through the slab, in a steady state is $(\frac{A ( T _{2} - T _{1} ) K}{x}) f$ , then $f$ is equal to

A body takes $4 min$ to cool from $6 1^{\circ} C$ to $5 9^{\circ} C$ . If the temperature of the surroundings is $3 0^{\circ} C$ , then the time taken by the body to cool from $5 1^{\circ} C$ to $4 9^{\circ} C$ is

(A)

4 min

(B)

3 min

(C)

8 min

(D)

6 min

JEE Main 2019

LEVELJEE Advanced

Two identical beakers A and B contain equal volumes of two different liquids at $6 0^{\circ} C$ each and left to cool down. Liquid in A has density of $8 \times 1 0^{2} kg/m^{3}$ and specific heat of $2000 J kg^{- 1} K^{- 1}$ while liquid in B has density of $1 0^{3} kg m^{- 3}$ and specific heat of $4000 J kg^{- 1} K^{- 1}$ . Which of the following best describes their temperature versus time graph schematically? (Assume the emissivity of both the beakers to be the same)

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

(A)

\frac{θ _{2} + θ _{1}}{2}

(B)

\frac{θ _{1}}{3} + \frac{2 θ _{2}}{3}

(C)

\frac{θ _{1}}{6} + \frac{5 θ _{2}}{6}

(D)

\frac{θ _{1}}{10} + \frac{9 θ _{2}}{10}

JEE Main 2013

LEVELJEE Main

If a piece of metal is heated to temperature $θ$ and then allowed to cool in a room which is at temperature $θ_{0}$ , the graph between the temperature $T$ of the metal and time $t$ will be closed to

Temperature difference of $12 0^{\circ} C$ is maintained between two ends of a uniform rod $A B$ of length $2 L$ . Another bent rod $P Q$ , of same cross-section as $A B$ and length $\frac{3 L}{2}$ is connected across $A B$ (see figure). In steady state, temperature difference between $P$ and $Q$ will be close to

(A)

4 5^{\circ}

(B)

3 5^{\circ} C

(C)

7 5^{\circ} C

(D)

6 0^{\circ} C

LEVELJEE Main

A liquid in a beaker has temperature $θ (t)$ at time $t$ and $θ_{0}$ is temperature of surroundings, then according to Newton's law of cooling, the correct graph between $lo g_{e} (θ - θ_{0})$ and $t$ is

Three rods of identical cross-section and lengths 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 $10 0^{\circ} C$ and the other at $0^{\circ} C$ (see figure). If the joints of the rod are at $7 0^{\circ} C$ and $2 0^{\circ} C$ in steady state 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

(A)

K_{1} : K_{3} = 2 : 3; K_{2} : K_{3} = 2 : 5

(B)

K_{1} < K_{2} < K_{3}

(C)

K_{1} : K_{2} = 5 : 2; K_{1} : K_{3} = 3 : 5

(D)

K_{1} > K_{2} > K_{3}

JEE Main 2021

LEVELJEE Main

In $5 min$ , a body cools from $7 5^{\circ} C$ to $6 5^{\circ} C$ at room temperature of $2 5^{\circ} C$ . The temperature of body at the end of next $5 min$ is ......... $^{\circ} C$ .

JEE Main 2021

LEVELJEE Main

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

(A)

\frac{2 K _{1} K _{2}}{K _{1} + K _{2}}

(B)

\frac{K _{1} + K _{2}}{2 K _{1} K _{2}}

(C)

\frac{K _{1} + K _{2}}{K _{1} K _{2}}

(D)

\frac{K _{1} K _{2}}{K _{1} + K _{2}}

LEVELJEE Main

One end of a thermally insulated rod is kept at a temperature $T_{1}$ and the other at $T_{2}$ . The rod is composed of two sections of lengths $l_{1}$ and $l_{2}$ and thermal conductivities $K_{1}$ and $K_{2}$ respectively. The temperature at the interface of the two sections is

(A)

\frac{( K _{2} l _{2} T _{1} + K _{1} l _{1} T _{2} )}{( K _{1} l _{1} + K _{2} l _{2} )}

(B)

\frac{( K _{2} l _{1} T _{1} + K _{1} l _{2} T _{2} )}{( K _{2} l _{1} + K _{1} l _{2} )}

(C)

\frac{( K _{1} l _{2} T _{1} + K _{2} l _{1} T _{2} )}{( K _{1} l _{2} + K _{2} l _{1} )}

(D)

\frac{( K _{1} l _{1} T _{1} + K _{2} l _{2} T _{2} )}{( K _{1} l _{1} + K _{2} l _{2} )}

LEVELJEE Main

A long metallic bar is carrying heat from one of its ends to the other end under steady-state. The variation of temperature $θ$ along the length $x$ of the bar from its hot end is best described by which of the following figure.

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

(A)

Rayleigh Jeans law

(B)

Planck's law of radiation

(C)

Stefan's law of radiation

(D)

Wien's law

LEVELJEE Main

Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K, respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

A metallic sphere cools from $5 0^{\circ} C$ to $4 0^{\circ} C$ in $300 s$ . If atmospheric temperature around is $2 0^{\circ} C$ , then the sphere's temperature after the next $5 min$ will be close to

(A)

3 1^{\circ} C

(B)

3 5^{\circ} C

(C)

2 8^{\circ} C

(D)

3 3^{\circ} C

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A body takes 4 min to cool from 61∘C to 59∘C. If the temperature of the surroundings is 30∘C, then the time taken by the body to cool from 51∘C to 49∘C is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } In 5 min, a body cools from 75∘C to 65∘C at room temperature of 25∘C. The temperature of body at the end of next 5 min is ......... ∘C.

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two identical metal wires of thermal conductivities K1​ and K2​ respectively are connected in series. The effective thermal conductivity of the combination is

The earth radiates in the infra-red region of the spectrum. The spectrum is correctly given by

Two spheres of the same material have radii 1 m and 4 m and temperatures 4000 K and 2000 K, respectively. The ratio of the energy radiated per second by the first sphere to that by the second is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } A metallic sphere cools from 50∘C to 40∘C in 300 s. If atmospheric temperature around is 20∘C, then the sphere's temperature after the next 5 min will be close to

A body takes $4 min$ to cool from $6 1^{\circ} C$ to $5 9^{\circ} C$ . If the temperature of the surroundings is $3 0^{\circ} C$ , then the time taken by the body to cool from $5 1^{\circ} C$ to $4 9^{\circ} C$ is

In $5 min$ , a body cools from $7 5^{\circ} C$ to $6 5^{\circ} C$ at room temperature of $2 5^{\circ} C$ . The temperature of body at the end of next $5 min$ is ......... $^{\circ} C$ .

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

A metallic sphere cools from $5 0^{\circ} C$ to $4 0^{\circ} C$ in $300 s$ . If atmospheric temperature around is $2 0^{\circ} C$ , then the sphere's temperature after the next $5 min$ will be close to