A slab of stone with an area \(0.36~\text{m}^{2}\) and thickness of \(0.1~\text{m}\) is exposed on the lower surface to steam at \(100^{\circ}\mathrm{C}\). A block of ice at \(0^{\circ}\mathrm{C}\) rests on the upper surface of the slab. In one hour \(4.8~\text{kg}\) of ice is melted. The thermal conductivity of the slab will be: (Given latent heat of fusion of ice \(= 3.36\times10^{5}~\text{JKg}^{-1}\))
1. \(1.29~\text{J/m/s/}^{\circ}\text{C}\)
2. \(2.05~\text{J/m/s/}^{\circ}\text{C}\)
3. \(1.02~\text{J/m/s/}^{\circ}\text{C}\)
4. \(1.24~\text{J/m/s/}^{\circ}\text{C}\)
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
A black body is at \(727^\circ\text{ C}.\) The rate at which it emits energy is proportional to:
1. | \((727)^2\) | 2. | \((1000)^4\) |
3. | \((1000)^2\) | 4. | \((727)^4\) |
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. | \(\dfrac{r^2\sigma(t+273)^4}{R^2}\) |
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 through the rod in a steady state is given by:
1.
2.
3.
4.
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. \(80\)