The temperature of the surface of the Sun is nearly \(6000~\text{K}\) and the amount of total energy emitted by the Sun per second is \(4\times10^{26}~\text{J}.\) If the temperature of the surface of the Sun is \(18000~\text{K},\) then the amount of thermal radiation emitted by the same will be:
1. \(3.24\times10^{28}~\text{W}\)
2. \(2.52\times10^{28}~\text{W}\)
3. \(8\times10^{26}~\text{W}\)
4. \(16\times10^{27}~\text{W}\)
| 1. | decreases from \(\dfrac12\) to \(\dfrac14\) |
| 2. | increases from \(\dfrac12\) to \(\dfrac34\) |
| 3. | decreases from \(\dfrac12\) to \(\dfrac13\) |
| 4. | increases from \(\Large\frac12\) to \(\Large\frac23\) |
| 1. | to make it attractive |
| 2. | for shining |
| 3. | to absorb all radiation from outside |
| 4. | to reflect all radiation from outside |
| 1. | \(2\) times more than the original value. |
| 2. | \(16\) times more than the original value. |
| 3. | \(\dfrac{1}{16}\) times the original value. |
| 4. | \(\dfrac{1}{2}\)times the original value. |
| Assertion (A): | A body that is a good radiator is also a good absorber of radiation at a given wavelength. |
| Reason (R): | According to Kirchhoff's law, the absorptivity of a body is equal to its emissivity at a given wavelength. |
| 1. | Both (A) and (R) are true and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are true but (R) is not the correct explanation of (A). |
| 3. | (A) is true but (R) is false. |
| 4. | Both (A) and (R) are false. |
| Assertion (A): | For small difference in absolute temperature, compared with the temperature itself, the net rate of transfer of energy from a body to its surrounding by radiation is directly proportional to the temperature difference. |
| Reason (R): | The net ratio of transfer of energy by radiation from a body (temperature \(T_b=T_S+\theta\)) to its surrounding (temperature \(T_S\)) is given by: \(\dfrac{dQ}{dt}=eA\sigma(T_b^4-T_S^4)\\ ~~~~~~~=eA\sigma\left\{(T_S+\theta)^4-T_S^4\right\}\\ ~~~~~~~\approx4eA\sigma T^3_S\theta,~\text{where }\theta\ll T_S.\) |
| 1. | Both (A) and (R) are True and (R) is the correct explanation of (A). |
| 2. | Both (A) and (R) are True but (R) is not the correct explanation of (A). |
| 3. | (A) is True but (R) is False. |
| 4. | (A) is False but (R) is True. |