Section A: Multiple Choice Questions (20 × 1 = 20 Marks)
1. The SI unit of heat is:
2. The temperature at which the volume of a gas becomes zero is:
3. The coefficient of linear expansion of a metal is α. Its coefficient of volume expansion is:
4. Water has maximum density at:
5. The specific heat capacity of water is:
6. The mode of heat transfer that doesn't require any medium is:
7. The latent heat of fusion of ice is:
8. Good conductors of heat are:
9. The Stefan-Boltzmann constant has value:
10. The triple point of water is at:
11. The principle of calorimetry is based on:
12. The coefficient of thermal conductivity for a perfect conductor is:
13. The rate of heat flow through a conductor is given by:
14. A black body is one which:
15. The temperature of the sun is determined by:
16. The amount of heat required to change 1 kg of a substance from solid to liquid at its melting point is called:
17. In conduction, heat is transferred by:
18. The value of 0 K in Celsius scale is:
19. The temperature at which the Fahrenheit and Celsius scales show the same reading is:
20. The quantity of heat required to raise the temperature of a body by 1°C is called:
Section B: Numerical Problems (5 × 2 = 10 Marks)
1. A steel rod of length 1 m has a coefficient of linear expansion α = 1.2 × 10⁻⁵ /°C. Calculate the increase in its length when its temperature is increased by 50°C.
Hint: Use the formula ΔL = L₀ × α × ΔT, where L₀ = 1 m, α = 1.2 × 10⁻⁵ /°C, ΔT = 50°C.
2. Calculate the amount of heat required to convert 100 g of ice at 0°C to water at 50°C. (Latent heat of fusion of ice = 336 J/g, specific heat of water = 4.2 J/g°C)
Hint: Two steps: (1) Heat to melt ice: Q₁ = m × L, (2) Heat to raise water temperature: Q₂ = m × c × ΔT. Total heat = Q₁ + Q₂.
3. A copper sphere of radius 10 cm is heated from 0°C to 100°C. Find the percentage increase in its volume. (Coefficient of linear expansion of copper = 1.7 × 10⁻⁵ /°C)
Hint: For volume expansion, γ = 3α. Percentage increase = (ΔV/V) × 100 = (γ × ΔT) × 100 = (3α × ΔT) × 100.
4. Two liquids A and B are at 30°C and 20°C respectively. When equal masses of these liquids are mixed, the temperature of the mixture is 26°C. Find the ratio of specific heat capacities of A and B.
Hint: Use principle of calorimetry: Heat lost by A = Heat gained by B. m × c_A × (30 - 26) = m × c_B × (26 - 20). Cancel m and solve for c_A/c_B.
5. A body cools from 80°C to 50°C in 10 minutes when the surrounding temperature is 20°C. What will be its temperature after next 10 minutes? (Assume Newton's law of cooling holds)
Hint: According to Newton's law of cooling, the rate of cooling is proportional to temperature difference. For equal time intervals, (T₁ - T₂)/log((T₁ - T₀)/(T₂ - T₀)) is constant, where T₀ is surrounding temperature.