Questions & explanations
1. Which of the following best describes the greenhouse effect in terms of radiation?
- Greenhouse gases reflect all incoming solar radiation back into space.
- Greenhouse gases absorb incoming ultraviolet radiation and re-emit it as visible light.
- Greenhouse gases allow shortwave solar radiation to reach Earth's surface but absorb and re-emit longwave infrared radiation emitted by Earth.
- Greenhouse gases trap all radiation from the Sun, causing the Earth to heat up uniformly.
Answer: Greenhouse gases allow shortwave solar radiation to reach Earth's surface but absorb and re-emit longwave infrared radiation emitted by Earth.
The greenhouse effect occurs because Earth's atmosphere is largely transparent to incoming shortwave solar radiation, which warms the surface. The surface then emits longwave infrared radiation. Greenhouse gases (such as CO₂, H₂O, CH₄) absorb some of this outgoing infrared radiation and re-emit it in all directions, including back toward the surface. This trapping of heat warms the lower atmosphere and surface. Option A is incorrect because greenhouse gases do not reflect all incoming radiation; reflection is mainly by clouds and the surface. Option B is incorrect because the primary absorption by greenhouse gases is in the infrared range, not ultraviolet. Option D is incorrect because greenhouse gases do not trap all solar radiation; they selectively absorb and re-emit the Earth's emitted longwave radiation, not incoming shortwave radiation.
2. Below is the heating curve for a pure substance (not drawn to scale). The curve consists of segments AB, BC, CD, DE, and EF. Segment AB shows temperature increase from -10°C to 0°C. Segment BC is horizontal at 0°C. Segment CD shows temperature increase from 0°C to 100°C. Segment DE is horizontal at 100°C. Segment EF shows temperature increase beyond 100°C. The substance is initially solid. Which of the following statements is correct?
- During segment BC, the substance exists only as a liquid.
- During segment CD, the substance exists as a mixture of solid and liquid.
- During segment DE, the substance exists only as a gas.
- During segment BC, the substance exists as a mixture of solid and liquid.
Answer: During segment BC, the substance exists as a mixture of solid and liquid.
Segment BC is horizontal at 0°C, which is the melting point of the substance. During melting, the substance absorbs heat to overcome intermolecular forces, so temperature remains constant while both solid and liquid phases coexist. Option A is incorrect because only liquid would be present after melting is complete. Option B is incorrect because CD shows the liquid phase heating up, not a mixture. Option C is incorrect because during boiling (DE), liquid and gas coexist, not only gas.
3. The heat energy required to convert 1 g of ice at 0°C into water at 0°C is called:
- A) Latent heat of vaporization
- B) Latent heat of fusion
- C) Specific heat
- D) Molar heat capacity
Answer: B) Latent heat of fusion
Latent heat of fusion is the heat energy needed to change a unit mass from solid to liquid at its melting point without a temperature change. Latent heat of vaporization is for liquid to vapour, specific heat involves temperature change, and molar heat capacity is per mole.
4. How much heat is required to convert 10 g of ice at -10°C into steam at 100°C? (Given: specific heat of ice = 0.5 cal g⁻¹ °C⁻¹, latent heat of fusion of ice = 80 cal g⁻¹, specific heat of water = 1 cal g⁻¹ °C⁻¹, latent heat of vaporization of water = 540 cal g⁻¹)
- A) 7200 cal
- B) 7250 cal
- C) 7350 cal
- D) 7450 cal
Answer: B) 7250 cal
Heat required in steps: (1) heating ice from -10°C to 0°C: 10×0.5×10 = 50 cal; (2) melting ice at 0°C: 10×80 = 800 cal; (3) heating water from 0°C to 100°C: 10×1×100 = 1000 cal; (4) vaporizing water at 100°C: 10×540 = 5400 cal. Total = 50+800+1000+5400 = 7250 cal.
5. The amount of heat required to raise the temperature of 1 mole of a substance by 1°C is called its:
- A) Specific heat capacity
- B) Molar heat capacity
- C) Thermal capacity
- D) Latent heat
Answer: B) Molar heat capacity
Molar heat capacity is defined as the heat required to raise the temperature of one mole of a substance by 1°C (or 1 K). Specific heat capacity is per unit mass, thermal capacity is for the entire body, and latent heat is associated with phase change.
6. Two bodies A and B are in thermal contact. They have the same temperature. Which of the following statements is correct?
- A) They have the same heat content.
- B) They have the same internal energy.
- C) They are in thermal equilibrium.
- D) They have the same specific heat capacity.
Answer: C) They are in thermal equilibrium.
Temperature is the measure of average kinetic energy; when two bodies have the same temperature, they are in thermal equilibrium. Heat content, internal energy, and specific heat capacity depend on mass and material properties, not just temperature.
7. In a calorimeter experiment, 200 g of water at 20°C is taken. A hot metal piece at 100°C is added. The final temperature is 30°C. The water equivalent of the calorimeter is 20 g. What is the heat lost by the metal? (Specific heat of water = 1 cal g⁻¹ °C⁻¹)
- A) 2000 cal
- B) 2200 cal
- C) 2400 cal
- D) 1800 cal
Answer: B) 2200 cal
Heat gained by water and calorimeter = (mass of water + water equivalent) × specific heat × ΔT = (200+20) × 1 × (30-20) = 220 × 10 = 2200 cal. By calorimetry principle, heat lost by metal = heat gained = 2200 cal.
8. Between which temperatures does water show anomalous expansion?
- A) 0°C to 4°C
- B) 4°C to 100°C
- C) 0°C to 100°C
- D) -10°C to 0°C
Answer: A) 0°C to 4°C
Water exhibits anomalous expansion between 0°C and 4°C: it contracts when heated in this range. Beyond 4°C it expands normally. This behavior allows ice to float and protects aquatic life in cold climates.
9. Two slabs of thermal conductivities k₁ and k₂ and equal thickness d are placed in series. The equivalent thermal conductivity of the combination is:
- (k₁ + k₂)/2
- 2k₁k₂/(k₁ + k₂)
- √(k₁k₂)
- (k₁k₂)/(k₁ + k₂)
Answer: 2k₁k₂/(k₁ + k₂)
For slabs of equal thickness in series, total thermal resistance R = d/(k₁A) + d/(k₂A) = (d/A)(1/k₁+1/k₂). Equivalent conductivity k_eq satisfies 2d/(k_eq A) = R, so k_eq = 2k₁k₂/(k₁+k₂).
10. If the coefficient of linear expansion of a solid is α, then its coefficient of areal expansion is:
- A) α
- B) 2α
- C) 3α
- D) α/2
Answer: B) 2α
For isotropic solids, the areal expansion coefficient β is approximately twice the linear expansion coefficient α (β = 2α) because area is a two-dimensional quantity.
11. Kirchhoff's law of thermal radiation states that for a body in thermal equilibrium at a given temperature and wavelength, the ratio of its emissive power to absorptive power is:
- Different for different bodies
- Equal to the emissive power of a black body at that temperature and wavelength
- Equal to the product of its emissivity and temperature
- Constant but depends on the nature of the surface
Answer: Equal to the emissive power of a black body at that temperature and wavelength
Kirchhoff's law: e(λ,T)/a(λ,T) = E_black(λ,T) (the emissive power of a black body) and is the same for all bodies at the same temperature and wavelength.
12. A perfect black body is defined as one that:
- Reflects all incident radiation
- Absorbs all incident radiation of all wavelengths
- Emits only infrared radiation
- Has a perfectly black surface visible to the eye
Answer: Absorbs all incident radiation of all wavelengths
A black body absorbs all electromagnetic radiation incident on it, regardless of wavelength, and also emits radiation according to its temperature.