The temperature of water at the surface of a deep lake is \(2^{\circ} \mathrm{C}\). The temperature expected at the bottom is:
1. \(0^{\circ} \mathrm{C}\)
2. \(2^{\circ} \mathrm{C}\)
3. \(4^{\circ} \mathrm{C}\)
4. \(6^{\circ} \mathrm{C}\)

In a room containing air, heat can go from one place to another:

A solid at temperature T₁, is kept in an evacuated chamber at temperature T₂ > T₁ . The rate of increase of temperature of the body is proportional to

1. T₂ – T₁

2.   \(T^2_2 -T^2_1\)n

3.   \(T^3_2 -T^3_1\)

4.   \(T^4_2 -T^4_1\)

A rod \(\mathrm{A}\) has a coefficient of thermal expansion \((\alpha_A)\) which is twice of that of rod \(\mathrm{B}\) \((\alpha_B)\). The two rods have length \(l_A,~l_B\) where \(l_A=2l_B\). If the two rods were joined end-to-end, the average coefficient of thermal expansion is:
1. \(\alpha_A\)
2. \(\frac{2\alpha_A}{6}\)
3. \(\frac{4\alpha_A}{6}\)
4. \(\frac{5\alpha_A}{6}\)

The ice-point reading on a thermometer scale is found to be \(20^\circ,\) while the steam point is found to be \(70^\circ.\) When this thermometer reads \(100^\circ ,\) the actual temperature is:
1. \(80^\circ~\mathrm{C}\)
2. \(130^\circ~\mathrm{C}\)
3. \(160^\circ~\mathrm{C}\)
4. \(200^\circ~\mathrm{C}\)

The temperature at which the Celsius and Fahrenheit thermometers agree (to give the same numerical value) is:
1. \(-40^\circ\)
2. \(40^\circ\)
3. \(0^\circ\)
4. \(50^\circ\)

Two rods of identical dimensions are joined end-to-end, and the ends of the composite rod are kept at \(0^\circ\mathrm{ C}\) and \(100^\circ\mathrm{ C}\) (as shown in the diagram). The temperature of the joint is found to be \(40^\circ\mathrm{ C}.\) Assuming no loss of heat through the sides of the rods, the ratio of the conductivities of the rods \(K_1/K_2\) is:
                     
1. \(\frac32\)
2. \(\frac23\)
3. \(\frac11\)
4. \(\frac{\sqrt3}{\sqrt2}\)