Physics: Thermal Physics and Gases
Thermal physics and gases is the A-level Physics topic covering internal energy, specific heat capacity, specific latent heat, the absolute (kelvin) temperature scale, and the behaviour of ideal gases: Boyle's law, Charles's law, the pressure law, and the ideal gas equation pV = nRT. It also covers the kinetic theory model of a gas, which links the random motion of individual molecules to the macroscopic pressure and temperature of the gas as a whole through the Boltzmann constant. This sits within AQA's Further Mechanics and Thermal Physics module (7407/7408) and is examined through direct recall of definitions plus multi-step gas-law and energy-transfer calculations, including data from required practical 8 (investigating Boyle's and Charles's laws).
Before you start
Make sure you're comfortable with these topics first:
Method
- Identify which gas law applies: Boyle's law (pV = constant) at constant temperature, Charles's law (V/T = constant) at constant pressure, or the pressure law (p/T = constant) at constant volume; if more than one variable changes, use the ideal gas equation pV = nRT (or pV = NkT if the number of molecules, N, is given instead of the number of moles, n).
- Always convert temperature to kelvin before substituting into a gas law: T (in K) = theta (in degrees C) + 273. Never substitute a Celsius value directly into pV = nRT or any gas law.
- Convert every quantity to SI base units before substituting: pressure in Pa (1 atm = 1.01 x 10^5 Pa), volume in m^3 (1 cm^3 = 1 x 10^-6 m^3, 1 litre = 1 x 10^-3 m^3).
- For energy-transfer questions, decide whether the substance is changing temperature (use Q = m x c x delta T, specific heat capacity) or changing state at a constant temperature (use Q = m x l, specific latent heat); a question covering both needs two separate calculations added together.
- For molecular kinetic theory questions, connect the microscopic and macroscopic pictures: pV = (1/3) x N x m x (mean square speed), where N is the number of molecules and m is the mass of one molecule, gives the pressure of a gas from the motion of its molecules; mean kinetic energy per molecule = (3/2) x k x T links molecular kinetic energy directly to absolute temperature, where k is the Boltzmann constant.
- State the assumptions of the kinetic theory model whenever a question asks you to justify or evaluate it: a large number of molecules in random, rapid motion; negligible volume of the molecules compared with the volume of the gas; negligible forces between molecules except during collisions; collisions that are perfectly elastic (no kinetic energy lost); and a time of collision that is negligible compared with the time between collisions.
- Show every step of unit conversion and rearrangement explicitly: these questions carry method marks for correct substitution even when the final numerical answer is wrong.
Worked example
A sealed container of volume 2.00 x 10^-3 m^3 contains an ideal gas at a pressure of 1.50 x 10^5 Pa and a temperature of 17 degrees C. Calculate the number of moles of gas in the container, and hence the number of gas molecules present. (Molar gas constant R = 8.31 J K^-1 mol^-1; Avogadro constant NA = 6.02 x 10^23 mol^-1.)
- Convert the temperature to kelvin: T = 17 + 273 = 290 K.
- Rearrange the ideal gas equation pV = nRT to make n the subject: n = pV / (RT).
- Substitute the values, all in SI units: n = (1.50 x 10^5 x 2.00 x 10^-3) / (8.31 x 290) = 300 / 2409.9.
- Calculate n: n = 0.124 mol (3 s.f.); carry the unrounded value, 0.1245 mol, forward to reduce rounding error.
- Multiply by the Avogadro constant to find the number of molecules: N = n x NA = 0.1245 x 6.02 x 10^23.
- Final answer: N = 7.49 x 10^22 molecules (3 s.f.).
Practice questions
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Q1State the value of absolute zero in degrees Celsius.Show answer
Answer: -273 degrees C (0 K).
Q2State what is meant by the internal energy of a gas.Show answer
Answer: The sum of the randomly distributed kinetic and potential energies of all the molecules of the gas.
Q3Convert a temperature of 45 degrees C to kelvin.Show answer
Answer: 318 K (45 + 273).
Q4Calculate the energy needed to raise the temperature of 0.500 kg of water by 15.0 degrees C. (Specific heat capacity of water = 4200 J / (kg K).)Show answer
Answer: 3.15 x 10^4 J (Q = mc x delta T = 0.500 x 4200 x 15.0 = 31500 J).
Q5Calculate the energy required to melt 0.200 kg of ice at 0 degrees C. (Specific latent heat of fusion of ice = 3.34 x 10^5 J/kg.)Show answer
Answer: 6.68 x 10^4 J (Q = ml = 0.200 x 3.34 x 10^5 = 66800 J).
Q6A fixed mass of gas has a volume of 400 cm^3 at a pressure of 1.00 x 10^5 Pa. Calculate its volume if the pressure is increased to 2.50 x 10^5 Pa at constant temperature.Show answer
Answer: 160 cm^3 (Boyle's law: p1V1 = p2V2, so V2 = (1.00 x 10^5 x 400) / (2.50 x 10^5) = 160 cm^3).
Q7State two assumptions of the kinetic theory model of an ideal gas.Show answer
Answer: Any two of: molecules are in continuous random motion; the volume of the molecules is negligible compared with the volume of the gas; forces between molecules (except during collisions) are negligible; collisions between molecules, and with the container walls, are perfectly elastic.
Q8Calculate the mean kinetic energy of a gas molecule at a temperature of 300 K. (Boltzmann constant k = 1.38 x 10^-23 J/K.)Show answer
Answer: 6.21 x 10^-21 J (mean KE = (3/2) x k x T = 1.5 x 1.38 x 10^-23 x 300 = 6.21 x 10^-21 J).
Exam-style questions
Written in the style of a A Level Science exam paper, with a full mark scheme.
A student heats 0.150 kg of ice, initially at -10.0 degrees C, until it becomes water at 20.0 degrees C, with no energy lost to the surroundings. Calculate the total energy required. (Specific heat capacity of ice = 2100 J / (kg K); specific latent heat of fusion of ice = 3.34 x 10^5 J/kg; specific heat capacity of water = 4200 J / (kg K).)
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A sealed syringe contains 6.00 x 10^-5 m^3 of an ideal gas at a pressure of 1.00 x 10^5 Pa and a temperature of 300 K. The gas is compressed at constant temperature until its pressure is 4.00 x 10^5 Pa. (a) Calculate the new volume of the gas. (b) Calculate the number of gas molecules in the syringe. (Boltzmann constant k = 1.38 x 10^-23 J/K.)
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Explain, in terms of the motion of gas molecules, why the pressure exerted by a fixed mass of gas increases when the gas is heated at constant volume.
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