Radiation MCQ Quiz - Objective Question with Answer for Radiation - Download Free PDF

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:

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.

Explanation:

Black Body in Thermal Radiation

Definition: A black body in the context of thermal radiation is an idealized object that absorbs all incident radiation, regardless of the wavelength or angle of incidence. It also emits radiation in a manner that is characterized solely by its temperature, and it emits the maximum possible radiation at a given temperature. This emission follows Planck's law of black-body radiation, making the black body an essential concept in thermodynamics and quantum mechanics.

Working Principle: The concept of a black body is fundamental in understanding thermal radiation and the interaction of matter with electromagnetic waves. When a black body absorbs all incident radiation, it does not reflect or transmit any part of the incoming energy. Instead, it converts this energy entirely into thermal energy, which then gets re-emitted as electromagnetic radiation. The spectrum and intensity of this emitted radiation depend solely on the temperature of the black body, following the laws of black-body radiation.

• Planck's Law: This law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature. It is a crucial principle in quantum mechanics.
• Wien's Displacement Law: This law states that the wavelength at which the emission of a black body spectrum is at its peak is inversely proportional to the temperature of the black body.
• Stefan-Boltzmann Law: This law states that the total energy radiated per unit surface area of a black body is proportional to the fourth power of its temperature.

Advantages:

• Provides a standard reference for the study of thermal radiation.
• Helps in understanding and measuring the thermal properties of real materials.
• Used in various scientific and engineering applications, including the calibration of radiometric devices.

Disadvantages:

• Real materials are not perfect black bodies; they reflect and transmit some radiation, making them less ideal for certain applications.
• Complex calculations and understanding of quantum mechanics are required to accurately describe black body radiation.

Applications: Black body concepts are widely used in astronomy, climate science, and the development of thermal imaging devices. They also play a critical role in the design of furnaces and in the study of stellar objects, where stars can be approximated as black bodies to understand their radiation characteristics.

Important information:

To analyze the other options:

• Option 2: An object with perfect thermal insulation does not necessarily act as a black body. Perfect thermal insulation implies that the object does not exchange heat with its surroundings, but it does not address the absorption and emission characteristics of radiation.
• Option 3: A surface that reflects all incident radiation without absorption is the opposite of a black body. Such a surface is known as a perfect reflector or a white body, which does not absorb any radiation and thus cannot be characterized as a black body.
• Option 4: A material that only emits visible light is not a black body. A black body emits radiation across the entire spectrum, including infrared and ultraviolet wavelengths, not just visible light.

Calculation:
Heat absorbed by radiation, heat generated, and heat lost through convection:

H_Radiation + H_Generated - H_Convection = H_Retained

α  + 7.1 - 2.5 = H_Retained

Heat Capacity (C) = H_Retained / ΔT

Substituting ΔT = 12.6 as given:

C = 1000 J/°C

Then, 

α +4.6 kW = 12.6 × 1000 W

⇒ α = 8kW

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 \(\frac{1}{{FA\sigma \left( {{T_1} + {T_2}} \right)\left( {T_1^2 + T_2^2} \right)}}\)

Concept:

Irradiation (G): The thermal radiation falling or incident upon a surface per unit time and per unit area is called irradiation

Radiosity (J): The total radiation energy leaving a surface per unit time per unit area is called radiosity.

Emissive Power (E): It is radiation energy leaving a surface.

J = Emitted Energy + Reflected part of incident energy

J = E + ρ G

For an opaque surface transmissivity (τ) = 0,

For any surface α + ρ + τ = 1

Where α = absorptivity, ρ = reflectivity, τ = transmissivity

Consider a small real body in thermal equilibrium with its surrounding blackbody cavity then by Kirchhoff's Law of radiation

⇒ absorptivity = emissivity ⇒ α = ϵ

∴ ρ + ϵ = 1, ρ = 1 - ϵ

J = E + (1 - ϵ) G

Calculation:

Given:

 radiosity (J) = 16 W/m², irradiation (G) = 24 W/m²,

Emissive power (E) = 12 W/m²

J = E + (1 - ϵ) G

16 = 12 + (1 - ϵ) 24

\(\epsilon= 1 - \frac{4}{{24}} = 0.83\)

J = E + ρG

J = εEb + ρG

Eb = Emissive power of a perfect black body

Concept:

From Wein's displacement law 

\({\lambda _{max}}T = 2898\;\mu m - k\left( {constant} \right)\)

Thus, \({\lambda _{peak}}T = \lambda _{peak}'T'\)

Calculation:

Given, 

Black body λpeak = 1.45 μm at 2000 K.

Now, \(\lambda _{peak}' = 2.90\;\mu m\)

1.45 × 2000 = 2.90 × T'

Concept:

F₁₁ + F₁₂ = 1

But F₁₁ = 0

∴ F₁₂ = 1

Now from reciprocating law

A₁ F₁₂ = A₂ F₂₁

Calculation:

\(\Rightarrow 4\pi r_1^2 \times I = 4\pi r_2^2 \times {F_{21}}\)

Concept:

Irradiation (G): Total radiation incident upon a surface per unit time per unit area.

Radiosity (J): Total radiation leaving a surface per unit time per unit area.

Radiosity comprises the original emittance from the surface plus the reflected portion of any radiation incident upon it.

J = E + ρG

J = εE_b + ρG

E_b = Emissive power of a perfect black body

α + ρ + τ = 1

For opaque body: τ = 0 ⇒ α + ρ = 1 ⇒ ρ = 1 - α = 1 - ε 

J = εE_b + (1 - ε)G = E + (1 - ε)G

Calculation:

Given:

G = 1000 W/m², E_b = 400 W/m², ϵ = 0.4

Explanation:  

Stephen's Boltzmann law:

According to Stefan’s law, the radiant energy emitted by a black body is directly proportional to the fourth power of its absolute temperature.

Q̇ = єσAT⁴

Where Q̇ is Radiate energy, σ is the Stefan-Boltzmann Constant, T is the absolute temperature in Kelvin, є is Emissivity of the material, and A is the area of the emitting body.

• Stefan's Law is used to accurately find the temperature Sun, Stars, and the earth.
• A black body is an ideal body that absorbs or emits all types of electromagnetic radiation.

From above it clear that the amount of radiation emitted by a perfectly black body is proportional to the fourth power of temperature on an ideal gas scale. Thus, option 3 is correct.

Explanation:

Let E be the total emissive power of the body and α be the absorptivity of the body.

α be the absorptivity of the body.

Emissivity (ϵ) is the ratio of emissive power of a non-black body to the black body.

ϵ = E/Eb

Kirchhoff’s law also holds for monochromatic radiation, for which

\(\frac{{{E_{\lambda 1}}}}{{{\alpha _{\lambda 1}}}} = \frac{{{E_{\lambda 2}}}}{{{\alpha _{\lambda 2}}}} = \frac{{{E_{b\lambda }}}}{{{\alpha _{b\lambda }}}} = \frac{{{E_{b\lambda }}}}{1}\)

∵ Absorptivity of a black body is one.

\(\therefore \frac{{{E_\lambda }}}{{{\alpha _\lambda }}} = {E_{b\lambda }} \Rightarrow {\alpha _\lambda } = \frac{{{E_\lambda }}}{{{E_{b\lambda }}}} = {\epsilon_\lambda }\)

Therefore, the monochromatic emissivity of a black body is equal to the monochromatic absorptivity at the same wavelength.

Eλ = αλEbλ

E = α EB

Important Points

According to Kirchhoff’s law, the ratio of total emissive power to absorptivity is constant for all bodies which are in thermal equilibrium with the surroundings. Therefore, it means that the emissivity of a body is equal to its absorptivity. 

Explanation:

Intensity of radiation:

The radiation intensity for emitted radiation I_e(θ, ϕ) is defined as the rate at which radiation energy dQ̇_e is emitted in the (θ, ϕ) direction per unit area normal to this direction and per unit solid angle about this direction. 

\({I_e}\left( {\theta ,\phi } \right)\; = \;\frac{{d{{\dot Q}_e}}}{{dA\cos \theta .d\omega }}\; = \;\frac{{d{{\dot Q}_e}}}{{dA\cos \theta \sin \theta \;d\theta d\phi }}\;\left( {\frac{W}{{{m^2}}}.sr} \right)\)

Emissivity (ϵ):

The emissivity of a surface represents the ratio of the radiation emitted by the surface at a given temperature to the radiation emitted by a blackbody at the same temperature.

For black body surface, ϵ = 1.

Irradiation (G):

The radiation flux incident on a surface from all directions is called irradiation G.

Absorptivity, reflectivity and transmissivity:

The fraction of irradiation absorbed by the surface is called the absorptivity α, the fraction reflected by the surface is called the reflectivity ρ, and the fraction transmitted is called the transmissivity τ.

\(\alpha + \rho + \tau \; = \;1\)

Explanation:

When thermal radiation falls onto an object,

• The radiation will be absorbed by the surface of the object, causing its temperature to change
• The radiation will be reflected from the surface of the body, causing no temperature change
• The radiation will pass completely through the object, causing no temperature change

Absorptivity (α) is a measure of how much of the radiation is absorbed by the body

Reflectivity (ρ) is a measure of how much is radiation is reflected

Transmissivity (τ) is a measure of how much radiation passes through the object.

Each of these parameters is a number that ranges from 0 to 1.

Absorptivity may be a function of wavelength and/or direction, and is related to the emissivity of the region by Kirchhoff's law. The absorptivity is identically equal to unity for black bodies and is independent of temperature and wavelength for gray bodies.

Concept:

• Thermal radiation is the transmission of heat in the form of radiant energy from one body to another body by the thermal motion of charged particles of matter.
• The mechanism of radiation is divided into 3 phases
  • Conversion of thermal energy of the hot source into electromagnetic waves
  • Passage of wave motion through intervening medium
  • Transformation of waves into heat
• Thermal radiation is limited to wavelengths ranging from 0.1 to 100 µm of the electromagnetic spectrum.

• It includes some portion of UV radiation (0.1 to 0.4 µm), entire visible radiation (0.4 to 0.7 µm), and entire infrared radiation (0.7 to 100 µm)