Heat Transfer Thermal Conductivity Questions

---

Very Short Answers Questions [1 Mark Questions]

Ques. Heat transfer through electromagnetic waves is known as

1. Conduction
2. Radiation
3. Convection
4. None of the above

Ans. The correct answer is b. Radiation

Explanation: The transfer of heat energy from one place to another in the form of electromagnetic waves without heating the intervening medium is known as Radiation.

Ques. What would be the thermal conductivity of gold at 20 degrees Celsius?

1. 35
2. 215
3. 315
4. 60

Ans. The correct answer is c. 315

Explanation: The thermal conductivity of gold at 20 ℃ is 315.

Ques. The physical quantity which describes the direction and rate of the temperature change around a particular location is known as

1. Isothermal property
2. Temperature quotient
3. Thermal equilibrium
4. Temperature gradient

Ans. The correct answer is d. Temperature gradient

Explanation: A temperature gradient is a physical quantity that describes how rapidly and in what direction the temperature changes in a particular area.

Ques. Which among the following has high electrical conductivity and high thermal conductivity?

1. Water
2. Plastic
3. Wood
4. Metal

Ans. The correct answer is d. Metal

Explanation: Due to the presence large number of free electrons in the metal its electrical and thermal conductivity is more.

Ques. Heat absorption causes the molecules of that body to ______ excess energy.

1. Gain
2. Loose
3. Remain constant
4. None of the above

Ans. The correct answer is a. Gain

Explanation: Due to the absorption of heat, the kinetic energy of the molecules of a substance increases. Hence, there is a gain in energy of the molecules.

---

Short Answers Questions [2 Marks Questions]

Ques. What are the three modes of heat transfer?

Ans. The three modes of heat transfer are

• Conduction: In this process of heat transfer, heat energy is transferred from one part of a body to another part without the movement of the particles from their mean position.
• Convection: In this process of heat transfer, heat energy is transferred from one part of a body to another part of a fluid i.e. liquid or gas by the movement of the particles of the fluid.
• Radiation: In this process of heat transfer, the heat energy is radiated in the form of electromagnetic radiation and travels from one place to another place without heating the intervening medium.

Ques. What is the effect of the change in density in temperature?

Ans. The density of a substance is defined as the mass per unit volume. Since volume changes with the temperature while its mass remains constant, then the density of the substance changes with temperature.

Ques. Define thermal stress. What is the formula of thermal stress?

Ans. If we clamp the ends of a rod rigidity to prevent its expansion or contraction and then exchange the temperature, tensile or compressive stress developed is called thermal stress.

The formula of thermal stress is given by

Thermal stress = - αℽΔT

Where

• α is the coefficient of linear expansion
• ℽ is the coefficient of volume expansion
• ΔT is the change in temperature

Check Out:

---

Long Answers Questions [3 Marks Questions]

Ques. What are the factors affecting thermal conductivity?

Ans. The thermal conductivity of a material is affected by the following factors

1. Material Composition: Thermal conductivity of a material depends on the atomic structure of the material. Since different materials have different atomic or molecular structures, therefore they may have different thermal conductivity.
2. Temperature: With the increase in temperature, the kinetic energy of the molecules of the substance increases which leads to an increase in molecular motion, and hence, the thermal conductivity increases.
3. Density: Due to the closer packing of atoms or molecules, the density of the material increases, and hence the thermal conductivity increases.

Ques. How is energy transferred by conduction and give an example?

Ans. Conduction is the process through which heat energy is transferred from the hotter part of a body to the cooler part without the actual movement of the particle from its mean position.

The atoms in the hotter regions have more kinetic energy than their cooler neighbors. They warm their neighbors giving some of their energy. The neighbors warm their neighbors, and so on through the material. The atoms themselves do not move from one region of material to another, but their energy does.

Ques. A surveyor uses a steel measuring tape that is exactly 50.000 m long at a temperature of 20 ℃. What is its length on a hot summer day when the temperature is 35 ℃? (Coefficient of linear expansion of steel, α_steel = 1.2 x 10^-5 K^-1)

Ans. Given

• The original length of the steel measuring tape, L₀ = 50 m
• Change in temperature, ΔT = 35 - 20 = 15 ℃
• Coefficient of linear expansion of steel, α_steel = 1.2 x 10^-5 K^-1

The length of steel measuring tape when the temperature increased from 20 ℃ to 35 ℃ is given by

L = L₀ (1 + αΔT )

⇒ L = 50 (1 + 1.2 x 10^-5 x 15 ) = 50.009 m

---

Very Long Answers Questions [5 Marks Questions]

Ques. Due to spatial variation in purity, the thermal conductivity of the metal bar having a cross-sectional area of 4 x 10^-4 m² and length of 1 m decreases linearly along its length from 400 Wm^-1K^-1 at one end to 200 Wm^-1K^-1 at the other. Calculate the rate at which heat flows through the bar if the hot end is maintained at 200 ℃ and the cold end at 0 ℃.

Ans. Given

• The length of the metal bar, l = 1 m
• Cross-sectional area of the metal bar, A = 4 x 10^-4 m²

Since thermal conductivity decreases along the length linearly, then thermal conductivity per unit length

= (400 - 200)/1 = 200 Wm^-1K^-1

Therefore, thermal conductivity at distance x is given by

K = 400 - 200x

Using Fourier’s law the rate of heat flow through section dx is given by

Q = – kA \(\frac{dT}{dx}\)

⇒Q = – (400 – 200 x) x 4 x 10 ^{– 4} \(\frac{dT}{dx}\)

⇒ – dT = \(\frac{Qdx}{(400-200x) \times 4 \times 10^{-4}}\)

⇒ – ₂₀₀∫⁰ dT = \(\frac{Q}{4 \times 10^{-4}}\) ₀∫¹ \(\frac{Qdx}{(400-200x)}\)

⇒ – (0 – 200) = \(– \frac{Q}{4 \times 10^{-4}}\) [ln 200 – ln 400]

⇒ 200 = – \(\frac{Q}{800 \times 10^{-4}}\) [ln 200 – ln 400]

⇒ 200 x 800 x 10^-4 = Q [ln 400 – ln 200]

⇒ 16 = Q x ln 2

⇒ Q = 23.1 W

Ques. Two identical rectangular rods of metal are welded as shown in Figure (1) and 20 J of heat flows through the rods in 1 minute. How long would it take for 20 J heat to flow through the rods if they are welded as shown in Figure (2)?

Ans. Let R be the resistance of each rod.

In Figure (1), both the rods are connected in parallel, therefore equivalent resistance will be

1/R_P = 1/R + 1/R

⇒ R_P = R/2

So the rate of flow of heat in parallel combination is given by

Q = (T₁ - T₂)/R_P

⇒ dH/dt = (T₁ - T₂)/R_P

⇒ 20/60 = (100 - 0)/(R/2)

⇒ R = 600 ℃/W

In Figure (2), both the rods are connected in series, therefore equivalent resistance will be

1/R_s = R + R

⇒ R_s = 2R

So the rate of flow of heat in series combination is given by

Q = (T₁ - T₂)/R_S

⇒ dH/dt = (T₁ - T₂)/R_S

⇒ 20/dt = (100 - 0)/2R

⇒ 20/dt = 100/2R

⇒ 20/dt = 100/(2 x 600)

⇒ 20/dt = 100/1200

⇒ dt = 240 seconds = 4 minutes

Ques. An 850 W consumer coffee maker can make 10 cups (1.75 liters) of 80 ℃ coffee from 20 ℃ tap water in 10 minutes. What percentage of the electrical energy consumed actually makes it to the coffee?

Ans. Mass of the water, m = density x volume

⇒ m = 1000 x 1.75 x 10^-3 = 1.75 kg

The specific heat of water, c = 4200 J/kg℃

Change in temperature, ΔT = 80 - 20 = 60 ℃

Heat gain by the water, H = mcΔT

⇒ H = 1.75 x 4200 x 60 = 441000 Joule

Now energy consumed by device in 10 minutes, E = P x t

⇒ E = 850 x 10 x 60 = 510000 J

Therefore percentage of energy used = energy used (H)/Totale energy supply (E) x 10%

⇒ Percentage of energy used = (441000/510000) x 100 = 86.5%

---

Previous Year Questions

1. Dimensional formula of Stefan's constant is...[Keam]
2. Cannizzaro reaction is not given by...[IIT JEE 1983]
3. Letters in the word HULULULU are rearranged. The probability of all three L being together is….[MHT CET 2018]
4. The reading of the ammeter for a silicon diode in the given circuit is​...[JEE Main 2018]
5. Alkyl halides react with dialkyl copper reagents to give...[AIEEE 2005]
6. The maximum number of equivalence relations on the set A={1, 2, 3} are..
7. Five equal resistances each of resistance R are connected as shown in the figure. A battery of V volts is connected between A and B. The current flowing in AFCEB will be..[Manipal 2007]
8. To use a transistor as an amplifier..[AIPMT 1991]
9. The variation of the rate of an enzyme catalyzed reaction with substrate concentration is correctly represented by graph..[Jee Main 2023]
10. The effect of rotation of the Earth on the value of acceleration due to gravity is​..

For Latest Updates on Upcoming Board Exams, Click Here: https://t.me/class_10_12_board_updates

---

Check-Out: