Two slabs \(A\) and \(B\) of equal surface area are placed one over the other such that their surfaces are completely in contact. The thickness of slab \(A\) is twice that of \(B\). The coefficient of thermal conductivity of slab \(A\) is twice that of \(B\). The first surface of slab \(A\) is maintained at \(100^{\circ}\text{C}\)$,$ while the second surface of slab \(B\) is maintained at \(25^{\circ}\text{C}\)$$. The temperature at the common surface will be:
1. \(62.5^{\circ}\text{C}\)
2. \(45^{\circ}\text{C}\)
3. \(55^{\circ}\text{C}\)
4. \(85^{\circ}\text{C}\)

Two rods, one made of aluminium and the other made of steel, having initial lengths \(l_1\) and \(l_2\) are connected together to form a single rod of length $l_1+l_2$. The coefficient of linear expansion for aluminium and steel are ${\alpha }_a$ and ${\alpha }_s$ respectively. If the length of each rod increases by the same amount when their temperature is raised by \(t^\circ \mathrm{C},\) then the ratio \(\frac{l_1}{l_1+l_2}\) is:
1. $\frac{{\alpha }_s}{{\alpha }_a}$

2. $\frac{{\alpha }_a}{{\alpha }_s}$

3. $\frac{{\alpha }_a}{{\alpha }_a+{\alpha }_s}$

4. $\frac{{\alpha }_s}{{\alpha }_a+{\alpha }_s}$

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 \(0^{\circ}\text{C}~\text{and}~90^{\circ}\text{C},\) respectively. The temperature at the junction of the three rods will be:

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

The rate of heat emission from an ideal black body at temperature T is H. What will be the rate of emission of heat by another body of same size at temperature 2T and emissivity 0.25?

\(150\) g of ice at \(0^\circ \mathrm{C}\) is mixed with \(100\) g of water at a temperature of \(80^\circ \mathrm{C}.\) The latent heat of ice is \(80\) cal/g and the specific heat of water is \(1\) cal/g°C. Assuming no heat loss to the environment, the amount of ice that does not melt is:

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:

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\(=336~\text{kJ kg}^{-1}\))

Two identical bodies are made of a material whose heat capacity increases with temperature. One of these is at ${\mathrm{}}^{}$\(100^{\circ} \mathrm{C}\), while the other one is at ${\mathrm{}}^{}$\(0^{\circ} \mathrm{C}\). If the two bodies are brought into contact, then assuming no heat loss, the final common temperature will be:

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:

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)