One kilogram of ice at \(0^\circ \text{C}\) is mixed with one kilogram of water at \(80^\circ \text{C}.\) The final temperature of the mixture will be: (Take: Specific heat of water = \(4200~\text{J kg}^{-1}\text{K}^{-1},\) latent heat of ice\(=336~\text{kJ kg}^{-1}\))

1.	\(0^\circ \text{C}\)	2.	\(50^\circ \text{C}\)
3.	\(40^\circ \text{C}\)	4.	\(60^\circ \text{C}\)

The value of the coefficient of volume expansion of glycerin is \(5\times10^{-4}\) K^-1. The fractional change in the density of glycerin for a temperature increase of \(40^\circ \mathrm{C}\) will be:

The temperature of a body falls from \(50^{\circ}\text{C}\)$\mathrm{}$ to \(40^{\circ}\text{C}\)$\mathrm{}$ in \(10\) minutes. If the temperature of the surroundings is \(20^{\circ}\text{C},\)$\mathrm{ t}$hen the temperature of the body after another \(10\) minutes will be:
1. \(36.6^{\circ}\text{C}\)          
2. \(33.3^{\circ}\text{C}\)$\mathrm{}$
3. \(35^{\circ}\text{C}\)             
4. \(30^{\circ}\text{C}\)$\mathrm{}$

Two rods (one semi-circular and the other straight) of the same material and of the same cross-sectional area are joined as shown in the figure. The points \(A\) and \(B\) are maintained at different temperatures. The ratio of the heat transferred through a cross-section of a semi-circular rod to the heat transferred through a cross-section of a straight rod at any given point in time will be:
                 
1. \(2:\pi\)
2. \(1:2\)
3. \(\pi:2\)
4. \(3:2\)

The plots of intensity versus wavelength for three black bodies at temperatures \(T_1,T_2\) and \(T_3\) respectively are as shown. Their temperatures are such that:
           

Hot coffee in a mug cools from \(90^{\circ}\text{C}\) to \(70^{\circ}\text{C}\) in \(4.8\) minutes. The room temperature is \(20^{\circ}\text{C}.\) Applying Newton's law of cooling, the time needed to cool it further by \(10^{\circ}\text{C}\) should be nearly:

Four rods of the same material with different radii \(r\) and the length \(l\) are used to connect two heat reservoirs at different temperatures. In which of the following cases is the heat conduction fastest?
1. \(r = \frac{1}{3}~\text{cm}, l = \frac{1}{9}~\text{cm}\)
2. \(r =3~\text{cm}, l =9~\text{cm}\)
3. \(r =4~\text{cm}, l =8~\text{cm}\)
4. \(r =1~\text{cm}, l =1~\text{cm}\)

In a steel factory, it is found that to maintain \(M\) kg of iron in the molten state at its melting point, an input power \(P\) watt is required. When the power source is turned off, the sample completely solidifies in time \(t\) seconds. The latent heat of the fusion of iron is:

In the Arctic region, hemispherical houses called Igloos are made of ice. It is possible to maintain a temperature inside an Igloo as high as \(20^\circ \text{C}\) because:

Two holes are cut into a metal sheet. The diameters of the two holes are \(d_1\) and \(d_2\) \((d_1>d_2).\) If the temperature of the metal sheet is increased, then which of the following distance increases?