Assertion (A): A body is emitting primarily red light. As the temperature of body is increased it may emit primarily yellow light.
Reason (R): Rate of radiation emitted by a body increases as the temperature increases.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true based on Wien's Displacement Law \( (\lambda_{\text{max}} T = b) \), where increasing ( T ) shifts \( \lambda_{\text{max}} \) to shorter wavelengths (red to yellow). Reason (R) is true based on Stefan-Boltzmann law \( (P \propto T^4) \). However, (R) explains the total radiated power, not the peak wavelength shift, so it's not the correct explanation for (A). Both are true, but (R) does not explain (A).
Assertion (A): The land surfaces get heated and cooled quickly compared to oceans.
Reason (R): Land surfaces are practically opaque to solar radiation and only few inches of the ground is affected.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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Land has lower specific heat than water and absorbs solar radiation only at the surface, leading to rapid temperature changes. Water has high specific heat and radiation penetrates deeply. Both A and R are true, and R explains A.
Assertion (A): Bodies radiate heat at all temperature.
Reason (R): Rate of radiation of heat is proportional to the fourth power of absolute temperature.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
All bodies above 0 K radiate thermal energy. The Stefan-Boltzmann law states that the rate of radiation P is proportional to the fourth power of absolute temperature \(T^4\), i.e., \(P \propto T^4\). This law confirms that radiation occurs at any temperature above absolute zero and quantifies it. Thus, R explains A.
Assertion (A): For an ideal black body, both absorption coefficient and reflection coefficient are one.
Reason (R): Perfect absorbers are perfect reflectors.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
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A black body is defined as a perfect absorber (absorption coefficient = 1) and a perfect emitter, but it reflects no radiation (reflection coefficient = \(0\)).
Perfect absorbers are the opposite of perfect reflectors. Both Assertion (A) and Reason (R) are false.
Assertion (A): Heat radiations and light have identical properties.
Reason (R): A cold body does not radiate heat to the hotter surroundings.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Heat radiation (infrared) and visible light are both forms of electromagnetic waves, sharing properties like speed, reflection, and refraction. All bodies above 0 K radiate heat. A colder body radiates heat but receives more from hotter surroundings, leading to net heat gain. Thus, R is false.
Assertion (A): A body with large reflectivity is a poor emitter of heat radiations.
Reason (R): A body with large reflectivity is a poor absorber of heat.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Kirchhoff's law states that a good absorber is also a good emitter. A body with large reflectivity (R) is a poor absorber (A), since A = 1 - R (assuming no transmission). Therefore, a poor absorber is a poor emitter. Both Assertion (A) and Reason (R) are true, and (R) correctly explains (A).
Assertion (A): If temperature of any body is increased by \(10\%\), then there will be \(40\%\) increase in amount of radiation from its surface.
Reason (R): Equation \(\frac{\Delta E}{E} = 4 \frac{\Delta T}{T}\) also the for large percentage increase where \(E \propto T^4\).
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
According to the Stefan-Boltzmann law, `\(E \propto T^4\)`. If `\(T\)` increases by `\(10\%\)`, the new temperature `\(T' = 1.1T\)`. Then `\(E' \propto (1.1T)^4 = 1.4641T^4\)`. The percentage increase is `\(46.41\%\)`. So, Assertion (A) is false. The approximation `\(frac{\Delta E}{E} = 4 \frac{\Delta T}{T}\)` is valid only for small percentage changes in temperature, not for 'large' changes like `\(10\%\)`. Therefore, Reason (R) is also false.
Assertion (A): The amount of radiation from sun’s surface varies as the fourth power of its absolute temperature.
Reason (R): The sun is a black body.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is a statement of the Stefan-Boltzmann law `\(E \propto T^4\)`. This law applies to black bodies. The Sun is an excellent approximation of a black body.
Therefore, both (A) and (R) are true, and (R) provides the correct explanation for why the Sun's radiation follows the fourth power of its absolute temperature.
Assertion (A): Two spheres of same material have radius \(r_1\) and \(r_2\) respectively and temperature \(4000\text{ K}\) and \(2000\text{ K}\) respectively. The energy radiated per second by first sphere is more than second sphere.
Reason (R): In thermal conduction, energy is transferred by transference of particles of conducting body.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
The power radiated by a sphere is `\(P = e \sigma (4\pi r^2) T^4\)`. The ratio of powers is `\(frac{P_1}{P_2} = \frac{r_1^2 (4000\text{ K})^4}{r_2^2 (2000\text{ K})^4} = 16 \frac{r_1^2}{r_2^2}\)`.
For `\(P_1 > P_2\)`, we need `\(16 r_1^2 > r_2^2\)` or `\(r_1 > r_2/4\)`. This is not universally true (e.g., if `\(r_1 = r_2/5\)`). Thus, Assertion (A) is false. Reason (R) describes convection, not conduction. Conduction involves energy transfer through molecular vibrations and collisions, not by the bulk transference of particles. Therefore, Reason (R) is also false.
A blackbody and a real body of identical dimensions are heated to same temperature. If ratio of rates of radiation of the blackbody and the real body is \(4 : 3\), then emissivity of the real body is equal to
1. \(0.25\)
2. \(0.50\)
3. \(0.75\)
4. \(0.67\)
View Answer
The rate of radiation of a blackbody is \(E_b = \sigma A T^4\) and for a real body is \(E = e \sigma A T^4\). Given \(\frac{E_b}{E} = \frac{4}{3}\), we have \(\frac{1}{e} = \frac{4}{3}\), which gives emissivity \(e = \frac{3}{4} = 0.75\).