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): A hot body is kept in surrounding. As it cools, its temperature falls from \(80^0 C\) to \(78^0 C\) in a time duration \(t_1\) and from \(50^0 C\) to \(48^0 C\) in time duration \(t_2\). The temperature of surrounding is constant \(20^0 C\), then \(t_1 > t_2\).
Reason (R): According to Newton’s law of cooling, rate of cooling depends only on the difference of temperature of the body and the surrounding.
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
Newton's law of cooling states that the rate of cooling `\(\frac{dT}{dt}\) ` is proportional to `\((T - T_s)\)`. For the first interval, average `\(T_{avg1} = 79^0 C\) ⇒ \(T_{avg1} - T_s) = 59^0 C\)`. For the second interval, average `\(T_{avg2} = 49^0 C\) ⇒ (T_{avg2} - T_s) = 29^0 C\)`. Since the temperature difference is greater in the first case, the rate of cooling is faster, meaning `\(t_1 < t_2\)`. So, Assertion (A) is false. Reason (R) states 'depends *only* on the difference', which is misleading as the rate also depends on factors like surface area and emissivity, embedded in the constant of proportionality. Thus, Reason (R) is also false under strict interpretation.
Assertion (A): Most of the heat transfer that is taking place on earth is by convection.
Reason (R): Mostly heat radiation from sun are obtained in infrared region.
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
Within the Earth's atmosphere and oceans, convection is indeed the primary mechanism for heat distribution, making Assertion (A) true. However, the Sun's peak radiation is in the visible light spectrum (around `\(500\text{ nm}\)`), not predominantly in the infrared region. Therefore, Reason (R) is false.
Assertion (A): Conduction usually takes place in solids, convection in liquids and gases and no medium is required for radiation.
Reason (R): In conduction and convection, heat is transferred from one place to other by actual motion of heated material.
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) correctly describes the primary media for each mode of heat transfer: conduction in solids, convection in fluids (liquids and gases), and radiation requiring no medium. So, (A) is true. Reason (R) is false because in conduction (especially in solids), heat is transferred by molecular vibrations and collisions, not by the actual bulk motion of heated material. Bulk motion is characteristic of convection.
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): When temperature difference across the two sides of a wall is increased, its thermal conductivity increases.
Reason (R): Thermal conductivity depends upon the temperature difference across the two sides of a wall.
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
Thermal conductivity is an intrinsic property of the material and does not depend on temperature difference. It depends on the material itself and its temperature. Both assertion (A) and reason (R) are incorrect statements. Hence, option (4) is correct.
Assertion (A): Specific heat of a body may be greater than its thermal capacity.
Reason (R): Mass of a body may be less than unity.
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
Thermal capacity is \(C = mc\), where \(m\) is mass and \(c\) is specific heat. If \(m < 1\) (e.g., in kg), then \(c\) will be numerically greater than \(C\). Thus, (A) is true. (R) states mass can be less than unity, which is true and correctly explains (A).
Assertion (A): Melting of solid causes no change in internal kinetic energy.
Reason (R): Latent heat is the heat required to melt a unit mass of solid.
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
During melting at constant temperature, the average kinetic energy of molecules (related to temperature) remains constant.
Latent heat increases potential energy. So (A) is true. (R) correctly defines latent heat.
However, (R) does not explain why kinetic energy remains unchanged.
Assertion (A): If one gram of ice at \(0^{\circ}\text{C}\) is mixed with one gram of water at \(80^{\circ}\text{C}\), then the final temperature of mixture will be \(0^{\circ}\text{C}\).
Reason (R): Latent heat of ice is \(540\text{ cal/g}\).
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 to melt 1g ice at \(0^{\circ}\text{C}\text{ is }1 \times 80\text{ cal/g} = 80\text{ cal}\). Heat from 1g water cooling from \(80^{\circ}\text{C}\text{ to }0^{\circ}\text{C}\text{ is }1 \times 1 \times 80 = 80\text{ cal}\). All ice melts, final temperature is \(0^{\circ}\text{C}\). So (A) is true.
Latent heat of fusion of ice is \(80\text{ cal/g}\), not \(540\text{ cal/g}\). So (R) is false.