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:

1.	\(0.015\)	2.	\(0.020\)
3.	\(0.025\)	4.	\(0.010\)

Steam at \(100^{\circ}\mathrm{C}\) is injected into 20 g of \(10^{\circ}\mathrm{C}\) water. When water acquires a temperature of \(80^{\circ}\mathrm{C}\), the mass of water present will be: (Take specific heat of water =1 cal g^-1 \(^\circ\)C^-1 and latent heat of steam = 540 cal g^-1)
1. 24 g                       
2. 31.5g
3. 42.5 g                   
4. 22.5 g

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

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. 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: $\mathrm{\pi }$ 

2. 1: 2

3. $\mathrm{\pi }$: 2

4. 3: 2

The plots of intensity versus wavelength for three black bodies at temperatures ${\mathrm{T}}_1$, ${\mathrm{T}}_2$ and ${\mathrm{T}}_3$ respectively are as shown. Their temperatures are such that:
         

One kilogram of ice at \(0^\circ \mathrm{C}\) is mixed with one kilogram of water at \(80^\circ \mathrm{C}.\) The final temperature of the mixture will be: (Take: Specific heat of water = \(4200\) J kg^-1 K^-1, latent heat of ice\(=336\) kJ kg^-1)
1. \(0^\circ \mathrm{C}\)
2. \(50^\circ \mathrm{C}\)
3. \(40^\circ \mathrm{C}\)
4. \(60^\circ \mathrm{C}\)

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

Four rods of the same material with different radii r and length $\mathcal{l}$ are used to connect two heat reservoirs at different temperatures. In which of the following cases is the heat conduction fastest?

1. $r=\frac{1}{3}\mathrm{cm},$ $\mathcal{l}=\frac{1}{9}\mathrm{cm}$

2. r = 3 cm, $\mathcal{l}$ = 9 cm

3. r = 4 cm, $\mathcal{l}$ = 8 cm

4. r = 1 cm, $\mathcal{l}$ = 1 cm

Three rods made of the same material, having the same cross-sectional area but different lengths 10 cm, 20 cm and 30 cm are joined as shown. The temperature of the junction will be:-

   
1. \(10.8^{\circ}\mathrm{C}\)
2. \(14.6^{\circ}\mathrm{C}\)
3. \(16.4^{\circ}\mathrm{C}\)
4. \(18.2^{\circ}\mathrm{C}\)

Three rods made of the same material and having the same cross-section have been joined as shown in the figure. Each rod has the same length. The left and right ends are kept at \(0^{\circ}\mathrm{C}\) $and$ \(90^{\circ}\mathrm{C}\), respectively. The temperature at the junction of the three rods will be:

         
1. \(45^{\circ}\mathrm{C}\)
2. \(60^{\circ}\mathrm{C}\)
3. \(30^{\circ}\mathrm{C}\)
4. \(20^{\circ}\mathrm{C}\)$$