1. 1
   An electric kettle with a 2.0 kW heating element contains 0.50 kg of water, initially at 20 °C. Assume all the energy from the element goes into the water. The specific heat capacity of water is 4180 J kg⁻¹ K⁻¹ and its specific latent heat of vaporization is 2.26 × 10⁶ J kg⁻¹.

   (a)

   How long does the kettle take to bring the water to its boiling point of 100 °C?

   [1 mark]

   • A21 s
   • B105 s
   • C565 s
   • D84 s

   (b)

   While the water is boiling at 100 °C, the energy supplied mainly increases which quantity?

   [1 mark]

   • AThe average random kinetic energy of the water molecules
   • BThe temperature of the water
   • CThe intermolecular potential energy of the water molecules
   • DThe density of the liquid water

   (c)

   After the water starts boiling, the kettle is left switched on for a further 2.0 minutes before it switches off. Determine the mass of water that boils away in this time.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A sealed, rigid steel cylinder contains helium gas at 27 °C. The cylinder is heated until the gas reaches 327 °C. Treat helium as an ideal monatomic gas.

   (a)

   What is the change in temperature of the helium in kelvin?

   [1 mark]

   • A300 K
   • B27 K
   • C573 K
   • D600 K

   (b)

   What is the ratio (average kinetic energy of the atoms at 327 °C) / (average kinetic energy of the atoms at 27 °C)?

   [1 mark]

   • A1.4
   • B2.0
   • C4.0
   • D12

   (c)

   Determine the average kinetic energy of a helium atom at 327 °C, and explain why, for this gas, the internal energy increases by the same factor.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A single-glazed window pane has an area of 1.5 m² and a thickness of 4.0 mm. The thermal conductivity of glass is 0.96 W m⁻¹ K⁻¹. On a winter night the inner surface of the glass is at 12.0 °C and the outer surface is at 4.0 °C. The owner replaces it with a double-glazed unit of the same area: two 4.0 mm glass panes separated by a 12 mm layer of air, of thermal conductivity 0.025 W m⁻¹ K⁻¹. The temperature difference across the whole unit is again 8.0 °C.

   (a)

   Determine the rate of thermal energy transfer by conduction through the single-glazed pane.

   [3 marks]

   (b)

   Assuming a steady state, in which the same rate of energy transfer passes through each layer of the double-glazed unit, show that almost all of the 8.0 °C temperature difference occurs across the air layer, and determine the rate of conduction through the unit. Suggest why the actual energy loss through the unit is greater than this value.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   An astronomer studies a red star. Its spectrum has a peak intensity at a wavelength of 830 nm, its apparent brightness at the Earth is 1.1 × 10⁻⁸ W m⁻², and its distance from the Earth is estimated as 5.2 × 10¹⁸ m, with an uncertainty of about ±20%. For comparison, the Sun has a luminosity of 3.83 × 10²⁶ W, a radius of 6.96 × 10⁸ m and a surface temperature of 5800 K. Treat the star as a black body.

   (a)

   Determine the surface temperature, luminosity and radius of the star.

   [6 marks]

   (b)

   Compare the star with the Sun and evaluate how reliable your values of luminosity and radius are, given the data and the assumptions made.

   [6 marks]

   Total for question 4: 12 marks

End of questions