The quantities of heat required to raise the temperature of two solid copper spheres of radii \(r_1\) and \(r_2\) \((r_1=1.5~r_2)\) through \(1~\text{K}\) are in the ratio:
1. \(\frac{9}{4}\)
2. \(\frac{3}{2}\)
3. \(\frac{5}{3}\)
4. \(\frac{27}{8}\)

Three stars \(A,\) \(B,\) and \(C\) have surface temperatures \(T_A,~T_B\)and \(T_C\) respectively. Star \(A\) appears bluish, star \(B\) appears reddish and star \(C\) yellowish. Hence,

A deep rectangular pond of surface area A, containing water (density = \(\rho,\) specific heat capacity = \(s\)), is located in a region where the outside air temperature is at a steady value of \(-26^{\circ}\mathrm{C}\)$$. The thickness of the ice layer in this pond at a certain instant is \(x\). Taking the thermal conductivity of ice as \(k\), and its specific latent heat of fusion as \(L\), the rate of increase of the thickness of the ice layer, at this instant, would be given by:
1. \(\frac{26k}{x\rho L-4s}\)
2. \(\frac{26k}{x^2\rho L}\)
3. \(\frac{26k}{x\rho L}\)
4. \(\frac{26k}{x\rho L+4s}\)

An object kept in a large room having an air temperature of \(25^\circ \text{C}\) takes \(12\) minutes to cool from \(80^\circ \text{C}\) to \(70^\circ \text{C}.\) The time taken to cool for the same object from \(70^\circ \text{C}\) to \(60^\circ \text{C}\) would be nearly:
1. \(10\) min
2. \(12\) min
3. \(20\) min
4. \(15\) min

A slab of stone with an area \(0.36~\text{m}^{2}\)${\mathrm{}}^{}$ 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 \(= 3.36\times10^{5}~\text{JKg}^{-1}\)${\mathrm{}}^{}$)
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. \(1.24~\text{J/m/s/}^{\circ}\text{C}\)

Gravitational force is required for:
1. stirring of liquid
2. convection
3. conduction
4. radiation

Which of the following circular rods, (given radius \(r\) and length \(l\)) each made of the same material and whose ends are maintained at the same temperature will conduct the most heat:

Radiation energy corresponding to the temperature T of the sun is E. If its temperature is doubled, then its radiation energy will be:
1. 32 E
2. 16 E
3. 8 E
4. 4 E

A sphere maintained at a temperature of 600 K, has a cooling rate R in an external environment of 200 K temperature. If its temperature falls to 400 K, then its cooling rate will be:

1. $\frac{3}{16}R$

2. $\frac{16}{3}R$

3. $\frac{9}{27}R$

4. None 

If λ_m denotes the wavelength at which the radioactive emission from a black body at a temperature T K is maximum, then:

1. λ_m is independent of T

2. λ_m ∝ T

3. λ_m ∝ T^–1

4. λ_m ∝ T^{– 4}