Edexcel IAL Physics: Thermodynamics and Astrophysics — Practice Questions

These are original questions written for Marlbridge, in the style and at the standard of the examination. They are not reproduced past-paper questions — examination boards hold copyright in their own papers. Use these alongside the official past papers available free from your board.

Related: Thermodynamics revision notes

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Section A

1. Define specific heat capacity and specific latent heat of vaporisation. [4]

2. State the ideal gas equation in the form pV = NkT, defining N and k. [2]

Section B

3. 0.50 kg of water at 20 °C is heated to boiling and 0.10 kg is then vaporised. (c_water = 4200 J kg⁻¹ K⁻¹; L_v = 2.26 × 10⁶ J kg⁻¹)

(a) Calculate the energy needed to raise the temperature to 100 °C. [3] (b) Calculate the energy needed to vaporise 0.10 kg. [2] (c) Explain why the temperature does not rise during vaporisation. [3]

4. Explain what is meant by the internal energy of a gas, and state how it changes when an ideal gas is heated at constant volume. [4]

5. A star has a surface temperature of 8500 K and a radius of 1.4 × 10⁹ m. (σ = 5.67 × 10⁻⁸ W m⁻² K⁻⁴; Wien constant = 2.898 × 10⁻³ m K)

(a) Calculate the peak wavelength of its emission. [3] (b) Calculate its luminosity using Stefan’s law. [3] (c) Explain how the temperature and luminosity of a star can be used to place it on a Hertzsprung–Russell diagram. [3]

6. Explain how red shift is used to determine the recession velocity of a galaxy, and state Hubble’s law. [4]

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Section C

7. The equation ½mc̄² = (3/2)kT links the microscopic motion of gas molecules to macroscopic temperature, where m is the mass of one molecule and c̄² is the mean square speed.

(a) State what is meant by absolute zero, in terms of molecular kinetic energy. [2]

(b) Use the equation to explain why doubling the absolute temperature of a fixed mass of gas does not double the root-mean-square speed of its molecules. [3]

8. CORE PRACTICAL 14 investigates the relationship between the pressure and volume of a fixed mass of gas at constant temperature.

(a) State Boyle’s law. [2]

(b) A gas has a volume of 250 cm³ at a pressure of 1.0 × 10⁵ Pa. Calculate its new volume if the pressure is increased to 2.5 × 10⁵ Pa at constant temperature. [3]

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Answers

1. Specific heat capacity — the energy required to raise the temperature of 1 kg of a substance by 1 K, without a change of state [1] [1]. Specific latent heat of vaporisation — the energy required to change 1 kg of a substance from liquid to gas at constant temperature [1] [1].

2. pV = NkT [1], where N is the number of molecules and k is the Boltzmann constant, 1.38 × 10⁻²³ J K⁻¹ [1].

3. (a) E = mcΔθ = 0.50 × 4200 × 80 [1] [1] = 168 000 J [1]. (b) E = mL = 0.10 × 2.26 × 10⁶ [1] = 226 000 J [1]. (c) The energy supplied is used to overcome the intermolecular forces of attraction and separate the molecules [1], increasing the potential energy component of the internal energy [1]; the mean kinetic energy is unchanged, and temperature is a measure of mean kinetic energy [1].

4. The internal energy is the sum of the randomly distributed kinetic and potential energies of all the molecules in the body [1] [1]. For an ideal gas the potential energy is taken as zero, since there are no intermolecular forces [1]; heating at constant volume does no work, so all the energy supplied increases the kinetic energy of the molecules and therefore the temperature [1].

5. (a) λ_max = 2.898 × 10⁻³ ÷ 8500 [1] [1] = 3.4 × 10⁻⁷ m (340 nm, ultraviolet) [1]. (b) A = 4πr² = 4π(1.4 × 10⁹)² = 2.46 × 10¹⁹ m² [1]; L = σAT⁴ = 5.67 × 10⁻⁸ × 2.46 × 10¹⁹ × 8500⁴ [1] = 7.3 × 10²⁷ W [1]. (c) The H–R diagram plots luminosity (or absolute magnitude) against surface temperature, with temperature increasing to the left [1]. A star’s position on it identifies whether it is a main sequence star, a giant, a supergiant or a white dwarf [1], and therefore its stage of evolution and its mass relative to the Sun [1].

6. The observed wavelength of a known spectral line is longer than the laboratory value [1]; the fractional shift gives the recession velocity from z = Δλ/λ = v/c for non-relativistic speeds [1]. Hubble’s law states that v = H₀d [1] — a galaxy’s recession velocity is directly proportional to its distance, which is the principal evidence for an expanding universe [1].

7. (a) Absolute zero is the temperature at which molecules have the minimum possible kinetic energy [1], so that no further energy can be removed from the substance — its internal energy is at a minimum [1].

(b) Since ½mc̄² = (3/2)kT, the mean kinetic energy (and hence c̄²) is proportional to T [1], so the mean square speed doubles when T doubles — but c̄, the root-mean-square speed, is proportional to √T, not T [1]. Doubling T therefore increases the root-mean-square speed by a factor of only √2, not 2 [1].

8. (a) At constant temperature, the pressure of a fixed mass of gas is inversely proportional to its volume (pV = constant) [2].

(b) p₁V₁ = p₂V₂, so V₂ = p₁V₁ ÷ p₂ = (1.0 × 10⁵ × 250) ÷ (2.5 × 10⁵) [2] = 100 cm³ [1].

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Where marks are usually lost

• Using ΔT in °C incorrectly when a temperature in kelvin is required (differences are the same, absolute values are not).
• Forgetting to use the surface area 4πr² in Stefan’s law.
• Saying the internal energy of an ideal gas includes potential energy.
• Raising T to the wrong power in Stefan’s law.
• Assuming average molecular speed is proportional to temperature rather than to its square root.
• Forgetting that Boyle’s law only holds at constant temperature for a fixed mass of gas.