JEE Physics Transmission of Heat MCQs Set 01

Multiple Choice Questions (MCQs) for JEE Physics: Transmission of Heat

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Practice Transmission of Heat MCQs for JEE Physics

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Multiple Choice Questions

Question 1: Under steady state, the temperature of a body
(a) increases with time
(b) decreases with time
(c) does not change with time and is the same at all points of the body
(d) does not change with time but is different at different points of the body
Show Answer & Explanation

Answer: (d) does not change with time but is different at different points of the body

Explanation:
1. In steady state each point has a constant temperature, but a temperature gradient exists along the conductor.

Teacher's Note:
1. Steady state means no change with time, not uniform temperature.

Question 2: The coefficient of thermal conductivity depends upon
(a) density of the material
(b) area of the plate
(c) thickness of the plate
(d) material of the plate
Show Answer & Explanation

Answer: (d) material of the plate

Explanation:
1. Thermal conductivity \( K \) is a property of the material only; area and thickness appear separately in \( KA\Delta T/L \).

Teacher's Note:
1. K is a material constant.

Question 3: When two ends of a rod wrapped with cotton are maintained at different temperatures and after some time every point of the rod attains a constant temperature, then
(a) conduction of heat at different points stops because the temperature is not increasing
(b) the rod is a bad conductor of heat
(c) heat is being radiated from each point of the rod
(d) each point of the rod is giving heat to its neighbour at the same rate at which it is receiving heat
Show Answer & Explanation

Answer: (d) each point of the rod is giving heat to its neighbour at the same rate at which it is receiving heat

Explanation:
1. In steady state each element receives heat from one side and passes the same amount to the other side, so its temperature stays constant.

Teacher's Note:
1. Conduction continues in steady state.

Question 4: The lengths of two rods made of the same metal with the same cross-sectional area are 0.6 m and 0.8 m. The temperatures at the ends of the first rod are \( 90^\circ C \) and \( 60^\circ C \), and those of the second rod are \( 150^\circ C \) and \( 110^\circ C \). For which rod will the rate of conduction be greater?
(a) First
(b) Second
(c) Same for both
(d) None of the above
Show Answer & Explanation

Answer: (c) Same for both

Explanation:
1. First rod gradient \( = 30/0.6 = 50^\circ C/m \); second rod gradient \( = 40/0.8 = 50^\circ C/m \).
2. Same \( K \), \( A \) and gradient, so the rate is the same.

Teacher's Note:
1. Rate depends on the temperature gradient, not on temperature difference alone.

Question 5: The ratio of thermal conductivity of two rods of different materials is 5 : 4. The two rods have the same area of cross-section and the same thermal resistance. The lengths of the rods will be in the ratio
(a) 4 : 5
(b) 9 : 1
(c) 1 : 9
(d) 5 : 4
Show Answer & Explanation

Answer: (d) 5 : 4

Explanation:
1. Thermal resistance \( R = \dfrac{L}{KA} \) is the same, so \( L\propto K \).
2. \( L_1 : L_2 = 5 : 4 \).

Teacher's Note:
1. Equal resistance and equal area means L is proportional to K.

Question 6: The thermal conductivity of a material in the CGS system is 0.4. In steady state, the rate of flow of heat is 10 cal/s-cm\( ^2 \). The thermal gradient will be
(a) \( 10^\circ C/cm \)
(b) \( 12^\circ C/cm \)
(c) \( 25^\circ C/cm \)
(d) \( 20^\circ C/cm \)
Show Answer & Explanation

Answer: (c) \( 25^\circ C/cm \)

Explanation:
1. Heat flux \( = K\times\text{gradient} \).
2. Gradient \( = \dfrac{10}{0.4} = 25^\circ C/cm \).

Teacher's Note:
1. Flux per unit area equals K times gradient.

Question 7: Two rectangular blocks A and B of different metals have the same length and the same area of cross-section. They are kept in contact end to end. The temperature at the free end of A is \( 100^\circ C \) and at the free end of B is \( 0^\circ C \). If the ratio of their thermal conductivities is 1 : 3, then under steady state the temperature of the junction is
(a) \( 25^\circ C \)
(b) \( 50^\circ C \)
(c) \( 75^\circ C \)
(d) \( 100^\circ C \)
Show Answer & Explanation

Answer: (a) \( 25^\circ C \)

Explanation:
1. Same heat current: temperature drops are in the ratio of resistances, \( \Delta T_A : \Delta T_B = \dfrac1{K_A} : \dfrac1{K_B} = 3 : 1 \).
2. Drop across A \( = 75^\circ C \), so the junction is at \( 100-75 = 25^\circ C \).

Teacher's Note:
1. In series the same heat current flows and the temperature drop is proportional to thermal resistance \( L/KA \).

Question 8: Two vessels of different materials are similar in size in every respect. The same quantity of ice filled in them gets melted in 20 minutes and 30 minutes. The ratio of their thermal conductivities will be
(a) 1.5
(b) 1
(c) 2/3
(d) 4
Show Answer & Explanation

Answer: (a) 1.5

Explanation:
1. Same heat is needed, so rate \( \propto K \) and \( t\propto 1/K \).
2. \( \dfrac{K_1}{K_2} = \dfrac{30}{20} = 1.5 \).

Teacher's Note:
1. Equal heat needed: time is inversely proportional to K.

Question 9: Two rods A and B of equal lengths have their ends kept at the same temperatures, and their areas of cross-section are \( A_1 \) and \( A_2 \) and thermal conductivities \( K_1 \) and \( K_2 \). The rate of heat transmission in the two rods will be equal if
(a) \( K_1A_2 = K_2A_1 \)
(b) \( K_1A_1 = K_2A_2 \)
(c) \( K_1 = K_2 \)
(d) \( K_1A_1^2 = K_2A_2^2 \)
Show Answer & Explanation

Answer: (b) \( K_1A_1 = K_2A_2 \)

Explanation:
1. With equal \( L \) and \( \Delta T \): \( \dfrac{Q}{t} = \dfrac{KA\Delta T}{L} \), so equal rates need \( K_1A_1 = K_2A_2 \).

Teacher's Note:
1. Rate of heat flow \( \dfrac{Q}{t} = \dfrac{KA\,\Delta T}{L} \).

Question 10: In Searle's method for finding the thermal conductivity of metals, the temperature gradient along the bar
(a) is greater nearer the hot end
(b) is greater nearer the cold end
(c) is the same at all points along the bar
(d) increases as we go from the hot end to the cold end
Show Answer & Explanation

Answer: (c) is the same at all points along the bar

Explanation:
1. The bar is lagged so no heat is lost sideways; in steady state the gradient is uniform.

Teacher's Note:
1. Lagging makes the flow one-dimensional.

Question 11: If the ratio of the coefficients of thermal conductivity of silver and copper is 10 : 9, the ratio of the lengths up to which wax will melt in Ingen Hausz's experiment will be
(a) 6 : 10
(b) \( \sqrt{10} : 3 \)
(c) 100 : 81
(d) 81 : 100
Show Answer & Explanation

Answer: (b) \( \sqrt{10} : 3 \)

Explanation:
1. In Ingen Hausz's experiment \( K\propto l^2 \).
2. \( \dfrac{l_1}{l_2} = \sqrt{\dfrac{10}{9}} = \dfrac{\sqrt{10}}{3} \).

Teacher's Note:
1. Length of wax melted is proportional to the square root of K.

Question 12: The thickness of a metallic plate is 0.4 cm. The temperature difference between its two surfaces is \( 20^\circ C \). The quantity of heat flowing per second is 50 calories from 5 cm\( ^2 \) area. In the CGS system the coefficient of thermal conductivity will be
(a) 0.4
(b) 0.6
(c) 0.2
(d) 0.5
Show Answer & Explanation

Answer: (c) 0.2

Explanation:
1. \( K = \dfrac{Q\,d}{A\,\Delta T\,t} = \dfrac{50\times0.4}{5\times20} = 0.2 \).

Teacher's Note:
1. Rate of heat flow \( \dfrac{Q}{t} = \dfrac{KA\,\Delta T}{L} \).

Question 13: A piece of glass is heated to a high temperature and then allowed to cool. If it cracks, a probable reason for this is the following property of glass
(a) low thermal conductivity
(b) high thermal conductivity
(c) high specific heat
(d) high melting point
Show Answer & Explanation

Answer: (a) low thermal conductivity

Explanation:
1. Glass conducts heat poorly, so outer and inner layers cool unequally and contract by different amounts, causing stress and cracks.

Teacher's Note:
1. Uneven cooling creates thermal stress.

Question 14: Two walls of thicknesses \( d_1 \) and \( d_2 \) and 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 is
(a) \( \dfrac{k_1T_1d_2+k_2T_2d_1}{k_1d_2+k_2d_1} \)
(b) \( \dfrac{k_1d_1+k_2d_2}{T_1+T_2} \)
(c) \( \dfrac{k_1d_1T_1+k_2d_2T_2}{k_1d_1+k_2d_2} \)
(d) \( \dfrac{k_1d_1+k_2d_2}{k_1d_2+k_2d_1} \)
Show Answer & Explanation

Answer: (a) \( \dfrac{k_1T_1d_2+k_2T_2d_1}{k_1d_2+k_2d_1} \)

Explanation:
1. Equal heat flow: \( \dfrac{k_1(T_1-T)}{d_1} = \dfrac{k_2(T-T_2)}{d_2} \).
2. Solving, \( T = \dfrac{k_1T_1d_2+k_2T_2d_1}{k_1d_2+k_2d_1} \).

Teacher's Note:
1. Equate the heat currents through the two walls.

Question 15: A slab consists of two parallel layers of copper and brass of the same thickness and having thermal conductivities in the ratio 1 : 4. If the free face of brass is at \( 100^\circ C \) and that of copper at \( 0^\circ C \), the temperature of the interface is
(a) \( 80^\circ C \)
(b) \( 20^\circ C \)
(c) \( 60^\circ C \)
(d) \( 40^\circ C \)
Show Answer & Explanation

Answer: (a) \( 80^\circ C \)

Explanation:
1. Temperature drops \( \propto 1/K \): copper : brass \( = 4 : 1 \).
2. Copper drop \( = \tfrac45\times100 = 80^\circ C \), so the interface is at \( 80^\circ C \).

Teacher's Note:
1. In series the same heat current flows and the temperature drop is proportional to thermal resistance \( L/KA \).

Question 16: The temperature gradient in a rod of 0.5 m length is \( 80^\circ C/m \). If the temperature of the hotter end of the rod is \( 30^\circ C \), then the temperature of the cooler end is
(a) \( -40^\circ C \)
(b) \( -10^\circ C \)
(c) \( 10^\circ C \)
(d) \( 0^\circ C \)
Show Answer & Explanation

Answer: (b) \( -10^\circ C \)

Explanation:
1. Temperature difference \( = 80\times0.5 = 40^\circ C \).
2. Cooler end \( = 30-40 = -10^\circ C \).

Teacher's Note:
1. Multiply the gradient by the length to get the difference.

Question 17: On heating one end of a rod, the temperature of the whole rod will be uniform when
(a) \( K = 1 \)
(b) \( K = 0 \)
(c) \( K = 100 \)
(d) \( K = \infty \)
Show Answer & Explanation

Answer: (d) \( K = \infty \)

Explanation:
1. Temperature is uniform only for an ideal conductor, \( K\to\infty \).

Teacher's Note:
1. Infinite conductivity means no gradient.

Question 18: Snow is more heat insulating than ice because
(a) air is filled in the pores of snow
(b) ice is a worse conductor than snow
(c) air is filled in the pores of ice
(d) the density of ice is more
Show Answer & Explanation

Answer: (a) air is filled in the pores of snow

Explanation:
1. Snow has many air-filled pores, and air is a very poor conductor.

Teacher's Note:
1. Trapped air is the insulator.

Question 19: Two thin blankets keep more warmth than one blanket of thickness equal to the two. The reason is
(a) their surface area increases
(b) a layer of air is formed between the two blankets, which is a bad conductor
(c) they have more wool
(d) they absorb more heat from outside
Show Answer & Explanation

Answer: (b) a layer of air is formed between the two blankets, which is a bad conductor

Explanation:
1. The air layer between the blankets adds thermal resistance, since air is a bad conductor.

Teacher's Note:
1. Air gaps insulate.

Question 20: Ice formed over lakes has
(a) very high thermal conductivity and helps in further ice formation
(b) very low conductivity and retards further formation of ice
(c) a permission for quick convection and retards further formation of ice
(d) very good radiating power
Show Answer & Explanation

Answer: (b) very low conductivity and retards further formation of ice

Explanation:
1. Ice is a poor conductor, so it insulates the water below and slows further freezing.

Teacher's Note:
1. A bad conductor retards heat loss.

Question 21: Two rods of the same length and material transfer a given amount of heat in 12 s when they are joined end to end. When they are joined lengthwise (side by side), they will transfer the same heat under the same conditions in
(a) 24 s
(b) 3 s
(c) 1.5 s
(d) 48 s
Show Answer & Explanation

Answer: (b) 3 s

Explanation:
1. End to end (series): \( R_s = 2R \). Side by side (parallel): \( R_p = R/2 \).
2. Rate increases 4 times, so time \( = 12/4 = 3 \) s.

Teacher's Note:
1. Series resistances add, parallel conductances add.

Question 22: Wires A and B have identical lengths and circular cross-sections with \( r_A = 2r_B \). For a given temperature difference between the two ends, both wires conduct heat at the same rate. The relation between the thermal conductivities is
(a) \( K_A = 4K_B \)
(b) \( K_A = 2K_B \)
(c) \( K_A = K_B/2 \)
(d) \( K_A = K_B/4 \)
Show Answer & Explanation

Answer: (d) \( K_A = K_B/4 \)

Explanation:
1. \( K_Ar_A^2 = K_Br_B^2 \Rightarrow K_A\times4 = K_B \).
2. \( K_A = K_B/4 \).

Teacher's Note:
1. Rate of heat flow \( \dfrac{Q}{t} = \dfrac{KA\,\Delta T}{L} \).

Question 23: Two identical plates of different metals are joined to form a single plate whose thickness is double the thickness of each plate. If the coefficients of conductivity of each plate are 2 and 3 respectively, then the conductivity of the composite plate will be
(a) 5
(b) 2.4
(c) 1.5
(d) 1.2
Show Answer & Explanation

Answer: (b) 2.4

Explanation:
1. Series: \( K = \dfrac{2K_1K_2}{K_1+K_2} = \dfrac{2\times2\times3}{5} = 2.4 \).

Teacher's Note:
1. For equal thicknesses in series, K is the harmonic mean.

Question 24: If the radius and length of a copper rod are both doubled, the rate of flow of heat along the rod increases
(a) 4 times
(b) 2 times
(c) 8 times
(d) 16 times
Show Answer & Explanation

Answer: (b) 2 times

Explanation:
1. Rate \( \propto \dfrac{A}{L} \propto \dfrac{r^2}{L} \).
2. New \( = \dfrac{4}{2} = 2 \) times.

Teacher's Note:
1. Rate of heat flow \( \dfrac{Q}{t} = \dfrac{KA\,\Delta T}{L} \).

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