Assuming the sun to have a spherical outer surface of radius \(r,\) radiating like a black body at temperature \(t^\circ \text{ C},\) the power received by a unit surface of the earth (normal to the incident rays) at a distance \(R\) from the centre of the sun will be: (where \(\sigma\) is Stefan's constant)

1.	\(\dfrac{4\pi r^2\sigma t^4}{R^2}\)	2.	\(\dfrac{r^2\sigma(t+273)^4}{4\pi R^2}\)
3.	\(\dfrac{16\pi^2r^2\sigma t^4}{R^2}\)	4.	\(\dfrac{r^2\sigma(t+273)^4}{R^2}\)

A black body is at \(727^\circ\text{ C}.\) The rate at which it emits energy is proportional to:

A black body at 1227 °C emits radiations with maximum intensity at a wavelength of 5000 Å. If the temperature of the body is increased by 1000 °C, the maximum intensity will be observed at:

1. 4000 Å

2. 5000 Å

3. 6000 Å

4. 3000 Å

On a new scale of temperature, which is linear and called the \(\mathrm{W}\) scale, the freezing and boiling points of water are \(39^\circ ~\mathrm{W}\)$$and \(239^\circ ~\mathrm{W}\) respectively. What will be the temperature on the new scale corresponding to a temperature of \(39^\circ ~\mathrm{C}\) on the Celsius scale?
1. \(78^\circ ~\mathrm{C}\)
2. \(117^\circ ~\mathrm{W}\)
3. \(200^\circ ~\mathrm{W}\)
4. \(139^\circ ~\mathrm{W}\)

The two ends of a rod of length L and a uniform cross-sectional area A are kept at two temperatures T₁ and T₂ (T₁> T₂). The rate of heat transfer $\frac{\mathrm{dQ}}{\mathrm{dt}}$ through the rod in a steady state is given by:

1. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KL}({\mathrm{T}}_1-{\mathrm{T}}_2)}{\mathrm{A}}$

2. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{K}({\mathrm{T}}_1-{\mathrm{T}}_2)}{\mathrm{LA}}$

3. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\mathrm{KLA}({\mathrm{T}}_1-{\mathrm{T}}_2)$

4. $\frac{\mathrm{dQ}}{\mathrm{dt}}=\frac{\mathrm{KA}({\mathrm{T}}_1-{\mathrm{T}}_2)}{\mathrm{L}}$

A black body at \(227^{\circ}~\mathrm{C}\) radiates heat at the rate of \(7~ \mathrm{cal-cm^{-2}s^{-1}}\).  At a temperature of \(727^{\circ}~\mathrm{C}\), the rate of heat radiated in the same units will be:
1. \(60\)
2. \(50\)
3. \(112\)
4. \(80\)

The total radiant energy per unit area, normal to the direction of incidence, received at a distance \(R\) from the centre of a star of radius \(r,\) whose outer surface radiates as a black body at a temperature \(T\) K is given by: (Where \(\sigma\) is Stefan’s constant):
1. \(\dfrac{\sigma r^{2}T^{4}}{R^{2}}\)

2. \(\dfrac{\sigma r^{2}T^{4}}{4 \pi R^{2}}\)

3. \(\dfrac{\sigma r^{2}T^{4}}{R^{4}}\)

4. \(\dfrac{4\pi\sigma r^{2}T^{4}}{R^{2}}\)

A cylindrical metallic rod in thermal contact with two reservoirs of heat at its two ends conducts an amount of heat Q in time t. The metallic rod is melted and the material is formed into a rod of half the radius of the original rod. What is the amount of heat conducted by the new rod when placed in thermal contact with the two reservoirs at the same time?

1. Q /4

2. Q/16

3. 2Q

4. Q/2

Liquid oxygen at \(50\) K is heated up to \(300\) K at a constant pressure of \(1\) atm. The rate of heating is constant. Which one of the following graphs represents the variation of temperature with time?

1.		2.
3.		4.