ThermodynamicsEdexcel A-Level Physics: Topic test

20 questions, 54 marks

Edexcel A-Level Physics

Thermodynamics topic test

Total 54 marks

Name

Class

Date

1
An electric shower heater has a power of 8.4 kW. Cold water at 12 °C enters the heater at a flow rate of 0.060 kg s⁻¹. Assume that all of the electrical energy is transferred to the water. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹ and the specific latent heat of vaporisation of water is 2.26 × 10⁶ J kg⁻¹.
(a)
What is the rise in temperature of the water as it passes through the heater?
[1 mark]
A45 K
B33 K
C0.033 K
D3.3 × 10⁴ K
(b)
The same heater is used to turn water that is already at 100 °C into steam at 100 °C. What mass of steam is produced each second?
[1 mark]
A2.7 × 10² kg s⁻¹
B1.9 × 10¹⁰ kg s⁻¹
C0.060 kg s⁻¹
D3.7 × 10⁻³ kg s⁻¹
(c)
Explain why the temperature of the water stays constant while it is boiling, even though energy is still being supplied.
[2 marks]
Total for question 1: 4 marks
2
The air in a room contains nitrogen molecules at a temperature of 20 °C. Take 0 °C as 273 K. The Boltzmann constant is 1.38 × 10⁻²³ J K⁻¹.
(a)
What is the mean kinetic energy of a nitrogen molecule at this temperature?
[1 mark]
A6.1 × 10⁻²¹ J
B4.0 × 10⁻²¹ J
C1.2 × 10⁻²⁰ J
D4.1 × 10⁻²² J
(b)
The temperature of the room rises from 20 °C to 40 °C. By what factor does the mean kinetic energy of a molecule increase?
[1 mark]
A1.4
B2.0
C1.07
D0.93
(c)
Explain the difference between the internal energy of an ideal gas and the internal energy of a real liquid.
[2 marks]
Total for question 2: 4 marks
3
An air bubble of volume 2.0 cm³ is released from a diver at a depth where the pressure is 4.0 × 10⁵ Pa and the temperature is 280 K. It rises to the surface, where the pressure is 1.0 × 10⁵ Pa and the temperature is 290 K. Treat the air as an ideal gas and assume that no molecules enter or leave the bubble. The Boltzmann constant is 1.38 × 10⁻²³ J K⁻¹.
(a)
Calculate the volume of the bubble at the surface.
[3 marks]
(b)
Calculate the number of molecules in the bubble and the mean kinetic energy of a molecule at the surface.
[4 marks]
Total for question 3: 7 marks
4
A rigid, thermally insulated container holds 2.4 × 10²³ atoms of helium, which behaves as an ideal gas, at a temperature of 290 K. The volume of the container is 0.010 m³. A 20 W electric heater inside the container is switched on for 30 s and transfers all of its energy to the gas. The Boltzmann constant is 1.38 × 10⁻²³ J K⁻¹.
(a)
Calculate the temperature of the gas after the heater has been on for 30 s, and the mean kinetic energy of a helium atom at this temperature.
[6 marks]
(b)
Calculate the pressure of the gas before and after heating. Explain, in terms of the motion of the atoms, why the pressure increases when the gas is heated.
[6 marks]
Total for question 4: 12 marks
5
A sealed vessel of volume 5.0 × 10⁻³ m³ contains 3.0 × 10²³ molecules of oxygen, each of mass 5.3 × 10⁻²⁶ kg, at a pressure of 1.2 × 10⁵ Pa. The Boltzmann constant is 1.38 × 10⁻²³ J K⁻¹.
(a)
What is the mean square speed ⟨c²⟩ of the molecules?
[1 mark]
A3.8 × 10⁴ m² s⁻²
B3.4 × 10² m² s⁻²
C1.1 × 10⁵ m² s⁻²
D3.4 × 10⁵ m² s⁻²
(b)
What is the temperature of the gas?
[1 mark]
A1.4 × 10² K
B2.2 × 10² K
C2.9 × 10² K
D97 K
(c)
Explain, in terms of the motion of molecules, why the pressure of a fixed mass of gas doubles when its volume is halved at constant temperature.
[2 marks]
Total for question 5: 4 marks
6
The filament of a lamp is at a temperature of 2900 K. It may be treated as a black body with a surface area of 4.0 × 10⁻⁵ m². Wien's constant is 2.898 × 10⁻³ m K and the Stefan–Boltzmann constant is 5.67 × 10⁻⁸ W m⁻² K⁻⁴.
(a)
What is the wavelength at which the filament emits most intensely?
[1 mark]
A2.9 × 10⁻³ m
B8.4 m
C1.0 × 10⁻⁹ m
D1.0 × 10⁻⁶ m
(b)
What is the total power radiated by the filament?
[1 mark]
A1.9 × 10⁻⁵ W
B1.6 × 10² W
C6.6 × 10⁻⁹ W
D1.1 × 10² W
(c)
State what is meant by a black body radiator.
[2 marks]
Total for question 6: 4 marks
7
A thermal imaging camera is used to view a person standing in a room. The skin surface of the person is at a temperature of 306 K and has a total area of 1.8 m². Treat the skin and the surroundings as black bodies. The walls of the room are at 293 K. Wien's constant is 2.898 × 10⁻³ m K and the Stefan–Boltzmann constant is 5.67 × 10⁻⁸ W m⁻² K⁻⁴.
(a)
Calculate the wavelength at which the skin emits most intensely, and state in which region of the electromagnetic spectrum this lies.
[3 marks]
(b)
Calculate the power radiated by the skin. The surroundings also radiate towards the person; calculate the net power lost by the person's skin by radiation.
[4 marks]
Total for question 7: 7 marks
8
A solid copper sphere of radius 1.5 cm and mass 0.13 kg is painted matt black so that it behaves as a black body. It is heated to 800 K and then suspended in an evacuated chamber whose walls are very cold, so the radiation that the sphere absorbs from the walls can be ignored. The specific heat capacity of copper is 385 J kg⁻¹ K⁻¹. Wien's constant is 2.898 × 10⁻³ m K and the Stefan–Boltzmann constant is 5.67 × 10⁻⁸ W m⁻² K⁻⁴.
(a)
Calculate the power radiated by the sphere at 800 K and the initial rate at which its temperature falls. Explain why the rate of fall of temperature decreases as the sphere cools.
[6 marks]
(b)
Calculate the wavelength of maximum emission at 800 K. State how this wavelength and the total power radiated change when the sphere has cooled to 400 K. Explain, in terms of the energy of its atoms, why the temperature of the sphere falls as it radiates.
[6 marks]
Total for question 8: 12 marks

End of questions

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).