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): 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.
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.
Assertion (A): Water can be made to boil without heating.
Reason (R): Boiling point of water is lowered by decreasing pressure.
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
Boiling occurs when vapor pressure equals external pressure. Reducing external pressure lowers the boiling point of water. Thus, water can be made to boil at room temperature or even lower without external heating. Both (A) and (R) are true, and (R) correctly explains (A).
Assertion (A): When a hot liquid is mixed with a cold liquid, the temperature of the mixer is undefined for some time and then becomes nearly constant.
Reason (R): If two bodies at different temperature are mixed in a calorimeter, the total energy of the two bodies remains conserved.
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
When liquids of different temperatures are mixed, it takes time to reach thermal equilibrium, so temperature is not uniform initially. So (A) is true. In an ideal calorimeter, total energy is conserved. So (R) is true. However, (R) does not explain the time-dependent nature of temperature equilibration in (A).
Assertion (A): A bottle is filled with water at \(40^{\circ}\text{C}\text{ on opening it at moon, water will boil}\).
Reason (R): Atmospheric pressure on the surface of moon is zero and boiling point is proportional to pressure.
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 moon has a negligible atmosphere, leading to near-zero surface pressure. At such low pressures, water's boiling point decreases significantly. Consequently, water at \(40^{\circ}\text{C}\text{ would readily boil}\). Both (A) and (R) are true, and (R) provides the correct explanation for (A).
Assertion (A): The expanded length l of a rod of original length l_0 is not correctly given by assuming \(\alpha\) to be constant with T \( \l = \l_0 (1 + \alpha \Delta T)\), if \(\alpha \Delta T\) is large.
Reason (R): It is given by \(l = \l_0 \text{e}^{\alpha \Delta T}\), which cannot be treated as being approximately equal to \(l_0 (1 + \alpha \Delta T)\text{ for large value of }\alpha \Delta T\).
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 standard linear expansion formula \(ell = \ell_0 (1 + \alpha \Delta T)\text{ is an approximation valid for small }\alpha \Delta T\), derived from the exponential form \(ell = \ell_0 \text{e}^{\alpha \Delta T}\). If \(alpha \Delta T\) is large, this approximation fails. Both (A) and (R) are true, and (R) correctly explains (A).
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.