\(150\) 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:
1. | \(100\) g | 2. | \(0\) |
3. | \(150\) g | 4. | \(50\) g |
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:
1. | 4.2 minute | 2. | 3.8 minute |
3. | 3.2 minute | 4. | 2.4 minute |
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. | \(60^\circ \mathrm{C}\) |
Two identical bodies are made of a material whose heat capacity increases with temperature. One of these is at \(100^{\circ} \mathrm{C}\), while the other one is at \(0^{\circ} \mathrm{C}\). If the two bodies are brought into contact, then assuming no heat loss, the final common temperature will be:
1. | \(50^{\circ} \mathrm{C}\) |
2. | more than \(50^{\circ} \mathrm{C}\) |
3. | less than \(50^{\circ} \mathrm{C}\) but greater than \(0^{\circ} \mathrm{C}\) |
4. | \(0^{\circ} \mathrm{C}\) |
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:
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 \(50^{\circ}\mathrm{C}\) to \(40^{\circ}\mathrm{C}\) in 10 minutes. If the temperature of the surroundings is \(20^{\circ}\mathrm{C}\)hen the temperature of the body after another 10 minutes will be:
1. \(36.6^{\circ}\mathrm{C}\)
2. \(33.3^{\circ}\mathrm{C}\)
3. \(35^{\circ}\mathrm{C}\)
4. \(30^{\circ}\mathrm{C}\)
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. \(2:\pi\)
2. \(1:2\)
3. \(\pi:2\)
4. \(3:2\)
A wall is made up of two layers, A and B. The thickness of the two layers is the same, but the materials are different. The thermal conductivity of A is double that of B. If in thermal equilibrium, the temperature difference between the two ends is \(36^{\circ}\mathrm{C}\)hen the difference in temperature between the two surfaces of A will be:
1. \(6^{\circ}\mathrm{C}\)
2. \(12^{\circ}\mathrm{C}\)
3. \(18^{\circ}\mathrm{C}\)
4. \(24^{\circ}\mathrm{C}\)
The temperature of the two outer surfaces of a composite slab, consisting of two materials having coefficients of thermal conductivity K and 2K and thickness x and 4x, respectively are and ( > ). The rate of heat transfer through the slab, in a steady state is , with f which equals to:
1. 1
2.
3.
4.