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 \(100​​^\circ\text{C}.\)$$ A block of ice at \(0^{\circ}\text{C}\) 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. \(1.24~\text{J/m/s/}^{\circ}\text{C}\)

Two conducting slabs of heat conductivity \(K_{1} ~\text{and}~K_{2}\) are joined as shown in figure. If the temperature at the ends of the slabs are \(\theta_{1}~\text{and}~\theta_{2} \ (\theta_{1}   >   \theta_{2} ),  \) then the final temperature \( \left(\theta\right)_{m} \) of the junction will be:

A cup of coffee cools from \(90^{\circ}\text{C}\) $\mathrm{to}$ \(80^{\circ}\text{C}\) in \(t\) minutes, when the room temperature is \(20^{\circ}\text{C}.\)$\mathrm{}$ The time taken by a similar cup of coffee to cool from \(80^{\circ}\text{C}\) $\mathrm{to}$ \(60^{\circ}\text{C}\) at room temperature same at \(20^{\circ}\text{C}\) is:
1. \(\frac{10}{13}t\) 
2. \(\frac{5}{13}t\)
3. \(\frac{13}{10}t\)
4. \(\frac{13}{5}t\)

A piece of iron is heated in a flame. If it becomes dull red first, then becomes reddish yellow, and finally turns to white hot, the correct explanation for the above observation is possible by using:

In an experiment on the specific heat of a metal, a \(0.20~\text{kg}\) block of the metal at \(150^{\circ}\text{C}\) is dropped in a copper calorimeter (of water equivalent of \(0.025~\text{kg}\)) containing \(150~\text{cm}^{3}\) of water at \(27^{\circ}\text{C}.\) The final temperature is \(40^{\circ}\text{C}.\) The specific heat of the metal will be: 
(the heat losses to the surroundings are negligible)
1. \(0 . 40  ~ \text{Jg}^{- 1} \text{K}^{- 1}\)
2. \(0 . 43  ~ \text{Jg}^{- 1} \text{K}^{- 1}\)
3. \(0 . 54 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)
4. \(0 . 61 ~ \text{Jg}^{- 1} \text{K}^{- 1}\)

The temperature at which the Celsius and Fahrenheit thermometers agree (to give the same numerical value) is:

Which of the curves in the figure represents the relation between Celsius and Fahrenheit temperature?

1.		2.
3.		4.

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. \(\dfrac{9}{4}\)

2. \(\dfrac{3}{2}\)

3. \(\dfrac{5}{3}\)

4. \(\dfrac{27}{8}\)