Assertion (A): As the temperature of the blackbody increases, the wavelength at which the spectral intensity \(E_\lambda\) is maximum decreases.
Reason (R): The wavelength at which the spectral intensity will be maximum for a black body is proportional to the fourth power of its absolute temperature.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
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Assertion (A) is true according to Wien's displacement law, \(\lambda_{max} T = \text{constant}\). Reason (R) is false as \(\lambda_{max}\) is inversely proportional to temperature, not proportional to \(T^4\). \(E = \sigma T^4\) relates total emissive power to temperature.
Assertion (A): Two metallic spheres of same size, one of copper and the other of aluminium, heated to the same temperature, will cool at the same rate when they are suspended in the same enclosure.
Reason (R): The rate of cooling of a body depends only on the excess of temperature of the body over the surroundings.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is false because cooling rate depends on material properties like specific heat capacity and emissivity, which differ for copper and aluminium. Reason (R) is false.
Newton's Law of Cooling shows rate depends on surface area and emissivity, not just temperature difference.
Assertion (A): Colour of a glowing black body changes on increasing its temperature.
Reason (R): Spectral emissive power associated with each wavelength does not increase in same proportion on increasing temperature of the Black Body.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Assertion (A) is true due to Wien's displacement law; \(\lambda_{max}\) shifts to shorter wavelengths with increasing temperature. Reason (R) is true. Planck's law shows spectral emissive power increases disproportionately for different wavelengths with temperature. (R) explains (A) as this disproportionate increase causes the color shift.
A solid sphere of copper of radius ( R ) and a hollow sphere of the same material of inner radius ( r ) and outer radius ( R ) are heated to the same temperature and allowed to cool in the same environment.
Assertion (A): Hollow sphere cools faster than solid sphere.
Reason (R): \( \left( \frac{d\theta}{dt} \right) \propto \frac{1}{m} \).
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. Hollow sphere has less mass ( m ) but same surface area ( A ) as solid sphere. Reason (R) is true, cooling rate \( \frac{dT}{dt} \propto \frac{A}{m} \). Since ( A ) is constant, \( \frac{dT}{dt} \propto \frac{1}{m} \). Lower mass ( m ) means faster cooling. Thus, both are true and (R) explains (A).
Assertion (A): A sphere, a cube and a thin circular plate made of same material and of same mass are initially heated to \( 200^{\circ}\text{C} \), the plate will cool at fastest rate.
Reason (R): Rate of cooling \( = \frac{\rho A \sigma}{ms} (T^4 – T_0^4) ) ( \propto \) surface area. Surface area is maximum for circular plate.
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 because a thin plate has a larger surface area-to-mass ratio. Reason (R) states cooling rate \( \propto \) surface area, which is true \( \frac{dT}{dt} \propto \frac{A}{m}) \), and that a plate has the maximum surface area (for a given mass). Thus, both are true and (R) correctly explains (A).
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
View Answer
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.