Heat Transfer MCQ Quiz - Objective Question with Answer for Heat Transfer - Download Free PDF

Correct option is: (3) 5 / 3

In series, R_eq = R₁ + R₂ + R₃

= 1 / (2KA) + 1 / (KA) + 1 / (2KA)

= 4 / (2KA)

R_eq = 2 / (KA)

In series rate of heat flow is same

(3T − T₁) / R₁ = (3T − T) / R_eq

((3T − T₁) KA) / 1 = (2T) KA / 2

⇒ 6T − 2T₁ = T

⇒ T₁ = 5T / 2         ...(1)

Now, equate heat flow rate in 3^rd section and total section

(T₂ − T) / R₃ = (3T − T) / R_eq

((T₂ − T)(2KA)) / 1 = (2T KA) / 2

⇒ 2T₂ − 2T = T

⇒ T₂ = 3T / 2         ...(2)

By equation (1) and (2)

T₁ / T₂ = (5T / 2) / (3T / 2) = 5 / 3

Explanation:

Black Body:

• A black body is an idealized physical object that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. A black body also emits radiation in a characteristic spectrum that depends only on its temperature, as described by Planck's Law.

Emissive Power:

• Emissive power of a black body refers to the total energy radiated per unit surface area per unit time. This is given by the Stefan-Boltzmann Law, which states:

E = σT⁴

Where:

• E = Emissive power (W/m²)
• σ = Stefan-Boltzmann constant (5.67 × 10^-8 W/m²K⁴)
• T = Absolute temperature of the black body (in Kelvin)

Calculation:

If temperature doubles: T' = 2T

\( E' = \sigma (2T)^4 = 16 \cdot \sigma T^4 = 16E \)

Explanation:

Gray Body

• A grey body is a theoretical object that has an emissivity less than 1 but remains constant over all wavelengths of radiation. This means that while it does not emit radiation as perfectly as a black body (which has an emissivity of 1), its emissivity does not vary with the wavelength of the radiation it emits.

Emissivity:

• Emissivity is a measure of a material's ability to emit energy as thermal radiation. It is defined as the ratio of the radiation emitted by a surface to the radiation emitted by a black body at the same temperature. A black body, with an emissivity of 1, is an ideal emitter that radiates the maximum possible energy at any given temperature. Real objects have emissivities less than 1, indicating that they emit less thermal radiation than a black body.

Characteristics of a Gray Body:

• Constant Emissivity: The primary characteristic of a gray body is that its emissivity is constant and does not change with the wavelength of the radiation. This is in contrast to real materials, whose emissivity can vary significantly with wavelength.
• Less than Perfect Emission: A gray body does not emit radiation as efficiently as a black body. The emissivity of a gray body is less than 1, indicating that it emits a fraction of the energy that a black body would emit at the same temperature.
• Practical Approximation: The concept of a gray body is useful in practical applications because it simplifies the analysis of thermal radiation. By assuming a constant emissivity, engineers and scientists can more easily calculate the thermal radiation properties of materials.

Explanation:

Thermal Conductivity of Materials

• Thermal conductivity is a physical property of materials that measures their ability to conduct heat. It is defined as the amount of heat (in watts) that passes through a material with a given area and thickness when a temperature difference exists across the material. The unit of thermal conductivity is watts per meter per degree Celsius (W/m·°C).

Working Principle:

• The working principle of thermal conductivity involves the transfer of heat energy from the hotter part of the material to the cooler part. This transfer occurs through the vibration of atoms and molecules or through the movement of electrons in the case of metals. Materials with high thermal conductivity can transfer heat quickly and efficiently, while materials with low thermal conductivity are better insulators.

Aluminium:

• Aluminium is known for its high thermal conductivity. It is a metal with a thermal conductivity value of approximately 237 W/m·°C, which is significantly higher compared to other materials listed in the options. This high thermal conductivity makes aluminium an excellent material for applications requiring efficient heat transfer, such as heat exchangers, cooling systems, and electronic components.
• Aluminium's ability to conduct heat quickly is due to the presence of free electrons that can move easily through the material, transferring thermal energy from one part to another. This property is particularly useful in industries where rapid heat dissipation is critical to prevent overheating and maintain optimal performance.

Additional Information Option 1: Rubber

• Rubber is an insulating material with a very low thermal conductivity. Its thermal conductivity value is typically around 0.1-0.2 W/m·°C, which means it does not conduct heat well. This property makes rubber suitable for applications requiring thermal insulation, such as in the manufacture of heat-resistant gloves, mats, and seals.

Option 2: Air

• Air also has low thermal conductivity, approximately 0.024 W/m·°C. This makes it a poor conductor of heat and an excellent insulator. Air is commonly used in insulating applications, such as in double-glazed windows, where the trapped air layer helps reduce heat transfer between the interior and exterior of buildings.

Option 4: Wood

• Wood has a moderate thermal conductivity, typically around 0.12-0.15 W/m·°C. While not as insulating as rubber or air, wood does not conduct heat as efficiently as metals like aluminium. Wood’s thermal conductivity depends on its density and moisture content, but it is generally used in applications where moderate insulation is required, such as in building construction and furniture making.

Explanation:

Intensity of Radiation and the Inverse Square Law

Definition: The intensity of radiation refers to the amount of energy radiated per unit area per unit time. It is a fundamental concept in physics, particularly in the study of electromagnetic waves and thermal radiation.

Correct Option: Inverse Square Law

The correct answer to the statement "Intensity of radiation varies with the:" is option 1, which states that the intensity of radiation varies with the inverse square of the distance. This principle is known as the inverse square law.

Inverse Square Law:

The inverse square law is a physical principle that describes how the intensity of a physical quantity (such as radiation, light, sound, etc.) decreases as the distance from the source increases. According to this law, the intensity of radiation is inversely proportional to the square of the distance from the source. Mathematically, it can be expressed as:

I ∝ 1/d²

Where:

• I = Intensity of radiation
• d = Distance from the radiation source

This means that if the distance from the source is doubled, the intensity of radiation becomes one-fourth. Similarly, if the distance is tripled, the intensity becomes one-ninth, and so on.

Derivation and Explanation:

The inverse square law can be derived from the geometry of how radiation spreads out from a point source. Imagine a point source emitting radiation uniformly in all directions. The radiation travels outward in spherical waves. As the distance from the source increases, the surface area of the sphere over which the radiation is spread increases.

The surface area of a sphere is given by the formula:
A = 4πd²

Where:

• A = Surface area of the sphere
• d = Radius of the sphere (distance from the source)

As the radiation travels outward, its energy is distributed over the surface area of the sphere. Since the surface area increases with the square of the distance, the intensity of radiation (energy per unit area) decreases with the square of the distance. Therefore, the intensity of radiation at distance d is inversely proportional to d².

Applications of the Inverse Square Law:

• Astronomy: The inverse square law is crucial in astronomy for understanding the brightness of stars and other celestial objects. The apparent brightness of a star decreases with the square of the distance from the observer.
• Radiation Safety: In radiation safety, the inverse square law is used to determine safe distances from radiation sources to minimize exposure. By increasing the distance from a radiation source, the intensity of exposure decreases significantly.
• Acoustics: In acoustics, the inverse square law explains how the intensity of sound decreases as the distance from the sound source increases. This principle is important in designing audio systems and soundproofing environments.
• Lighting: In lighting design, the inverse square law helps in calculating the illumination levels from light sources at different distances. It is essential for setting up proper lighting in various environments.

The correct answer is 212° F.

• At 1 atmosphere of pressure (sea level), water boils at 100° C (212° F).
• When a liquid is heated, it eventually reaches a temperature at which the vapor pressure is large enough that bubbles form inside the body of the liquid. This temperature is called the boiling point.
  • Once the liquid starts to boil, the temperature remains constant until all of the liquid has been converted to a gas.

Important Points

• The boiling point of water depends on the atmospheric pressure, which changes according to elevation.
  • Water boils at a lower temperature as you gain altitude (e.g., going higher on a mountain).
  • Water boils at a higher temperature if you increase atmospheric pressure (coming back down to sea level or going below it).
• The boiling point of water also depends on the purity of the water.
  • Water that contains impurities (such as salted water) boils at a higher temperature than pure water. This phenomenon is called boiling point elevation.
  • It is one of the colligative properties of matter.

Key Points

• Liquids have a characteristic temperature at which they turn into solids, known as their freezing point.
  • Water freezes at 32° F or 0° C or 273.15 Kelvin.
• Pure, crystalline solids have a characteristic melting point, the temperature at which the solid melts to become a liquid.
• In theory, the melting point of a solid should be the same as the freezing point of the liquid.

Explanation:

In case of the counter-flow heat exchanger when the heat capacities of both the fluids are the same.

i.e. ṁ_hc_h = ṁ_cc_c

Q = ṁ_hc_h(T_h1 – T_h2) = ṁ_cc_c(T_c2 – T_c1)

⇒ (T_h1 – T_h2) = (T_c2 – T_c1)

⇒ (T_h1 – T_c2) = (T_h2 – T_c1)

⇒ ΔT₁ = ΔT₂

For parallel flow heat exchanger,  ΔT1 will always be greater than ΔT2.

Explanation:

Gases transfer heat by the collision of molecules.

As the temperature increases, the kinetic energy of molecules of gases also increases and eventually collision between molecules also increases which increases the thermal conductivity of gases.

∴ As temperature increases the thermal conductivity of gases increases.

For liquid and solids, generally as the temperature increases, the thermal conductivity decreases.

Concept:

Prandtl number Pr is defined as the ratio of momentum diffusivity to thermal diffusivity.

\(Pr = \frac{{\mu {C_p}}}{K} = \frac{{\left( {\frac{\mu }{\rho }} \right)}}{{\left( {\frac{K}{{\rho {C_p}}}} \right)}}\)

\(Pr = \frac{\nu }{\alpha } = \frac{{momentum\;diffusivity}}{{thermal\;diffusivity}}\)

In another way, we can define Prandtl number as, the ratio of the rate that viscous forces penetrate the material to the rate that thermal energy penetrates the material.

\(\frac{δ }{{{δ _T}}} = {\left( {Pr} \right)^{1/3}}\;\)where, δ is hydrodynamic boundary layer thickness and δ_T is thermal boundary layer thickness.

Calculation:

Given:

Pr = 0.7 

from, \(\frac{δ }{{{δ _T}}} = {\left( {Pr} \right)^{1/3}}\;\)=  \({0.7^{\frac{1}{3}}} = 0.88 < 1\)

thus, δ < δ_T .

When              P_r < 1               δ_T > δ 

                        P_r  > 1               δT < δ 

Explanation:

Prandtl member is the ratio of momentum diffusivity to thermal diffusivity.

\(Pr = \frac{\nu }{\alpha } = \frac{\mu }{{\frac{{\rho k}}{{\rho {C_p}}}}} = \frac{{\mu {C_p}}}{k}\)

Typical ranges of Prandtl member is listed below

Thermal conductivity of different metals in liquid state is given below

Sodium (Na) – 140 W/m-K

Potassium (K) – 100 W/m-K

Lithium (Li) – 85 W/m-K

Tin (Sn) – 64 W/m-K

Lead (Pb) – 36 W/m-K

Mercury ( Hg) – 8 W/m-K

So out of given options Sodium has highest thermal conductivity.

Concept:

Explanation:

• As we know the radiation travels with the speed of light, thus the rate of heat transfer is maximum in radiation in form of electromagnetic radiations

Explanation:

Insulation

• It is defined as a process of preventing the flow of heat from the body by applying insulator materials to the surface which controls the rate of heat transfer.
• The insulating ability of an insulator depends on various factors:
  • thickness of insulator
  • material of insulator
  • surrounding conditions
  • temperature difference  
• Generally, air packets are present in porous insulating materials.
• Since water which is a more conductive material is replacing air which is a less conductive material, so the overall insulating ability of the insulator will decrease. Most insulators are porous in nature.
• If it has been about Non-porous insulators then the insulating ability will remain unaffected.

Explanation:

Net radiation heat exchange between two bodies is given by:

Q̇ = AF × σ × (T₁⁴ - T₂⁴)

where F, A, σ are shape factor, Area and Stefan-Boltzmann constant respectively

Now explanding  (T14 - T24)

Q̇ = AF × σ × ((T1)²)² - (T2)²)²)

Q̇ = AF × σ × (T12 - T22) × (T12 + T22)

Q̇ = AF × σ × (T₁ - T₂)(T₁ + T₂) ×  (T12 + T22)

\(\dot Q =\frac{T_1-T_2}{\frac{1}{\sigma \times AF \times(T_1+T_2)\times(T_1^2+T_2^2)}}\)

Comparing with the electrical analogy \(i=\frac VR\)

We will get thermal resistance as \(\frac{1}{{FA\sigma \left( {{T_1} + {T_2}} \right)\left( {T_1^2 + T_2^2} \right)}}\)

Explanation:

• The variation in thermal conductivity of a material with temperature in the temperature range of interest is given by:
• k(T) = k0 (1 + βT) where β is called the temperature coefficient of thermal conductivity.
• The variation of temperature in a plane wall during steady one - dimensional heat conduction for the cases of constant and variable thermal conductivity is