5 g of water at \(30^{\circ} \mathrm{C}\) and 5 g of ice at \(-20^{\circ} \mathrm{C}\) are mixed together in a calorimeter. The water equivalent of the calorimeter is negligible, and the specific heat and latent heat of ice are 0.5 \(\text{cal/g}^{\circ} \mathrm{C}\) and 80 \(\text{cal/g}\), respectively. The final temperature of the mixture is:

1.	\(0^{\circ} \mathrm{C}\)	2.	\(-8^{\circ} \mathrm{C}\)
3.	\(-4^{\circ} \mathrm{C}\)	4.	\(2^{\circ} \mathrm{C}\)

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. \(18.2^{\circ}\mathrm{C}\)

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

A brass wire \(1.8\) m long at \(27\) °C is held taut with a little tension between two rigid supports. If the wire is cooled to a temperature of\(-39\) °C, what is the tension created in a wire with a diameter of \(2.0\) mm? (coefficient of linear expansion of brass \(=2.0 \times10^{-5}\) K^-1, Young's modulus of brass\(=0.91 \times10^{11}\) Pa)
1. \(3.8 \times 10^3\) N
2. \(3.8 \times 10^2\) N
3. \(2.9 \times 10^{-2}\) N
4. \(2.9 \times 10^{2}\) N

In an experiment on the specific heat of a metal, a 0.20 kg block of the metal at \(150^{\circ}\mathrm{C}\) is dropped in a copper calorimeter (of water equivalent of 0.025 kg) containing 150 \(c m^{3}\) of water at \(27^{\circ}\mathrm{C}\). The final temperature is \(40^{\circ}\mathrm{C}\). The specific heat of the metal will be: (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 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:
         

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 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. \(30^{\circ}\mathrm{C}\)$\mathrm{}$

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