Thermal physics: gases, systems and energy transfer
Key idea: Connect thermodynamic temperature and molecular motion to ideal-gas behaviour, internal energy, equilibrium, work, the thermodynamic laws and thermal-property energy balances.
Before you start: Energy & Fields objective chainQuantities & Measurement objective chain
By the end, you can
- Use the absolute thermodynamic scale and ideal-gas equations with particle and mole quantities.
- Apply the kinetic model to derive gas pressure and relate temperature to mean translational kinetic energy.
- Distinguish internal energy, temperature and heating, and explain thermal equilibrium.
- Apply work sign conventions and the zeroth and first laws without changing convention mid-solution.
- Use specific heat capacity and specific latent heat in thermal energy balances.
Starting-point self-check
1. Check your starting point
Attempt all six groups without notes and mark the first scale, particle-count, collision, energy-store or sign decision you cannot justify. Use the recorded topic diagnostic above when you want scoring and a personalised repair plan.
Ideal-gas equations, particles and moles 12(c)–(d)
Question 1
A gas has 0.200 mol at 300 K in 5.00 × 10⁻³ m³. Find its pressure and the number of molecules. Use R = 8.31 J mol⁻¹ K⁻¹ and Nₐ = 6.02 × 10²³ mol⁻¹.
Check the model response
p = nRT/V = 9.97 × 10⁴ Pa. N = nNₐ = 1.20 × 10²³. The equivalent particle form is pV = NkT because Nk = nR.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Ideal-gas equations, particles and moles 12(c)–(d)
Check this idea
Misconception: Celsius can be used directly in pV = NkT.
Repair: Ideal-gas equations require absolute thermodynamic temperature in kelvin.
Check this idea
Misconception: The particle and mole forms mix N with R or n with k.
Repair: Use pV = NkT or pV = nRT, linked by N = nNₐ and R = Nₐk.
worked example
3. Follow six worked models
Follow how each solution fixes the scale, gas amount, collision axis, system boundary or work convention before calculating.
Ideal-gas equations, particles and moles 12(c)–(d)
Model 1
A vessel contains 3.01 × 10²² molecules at 400 K and 1.00 × 10⁵ Pa. Find the volume using k = 1.38 × 10⁻²³ J K⁻¹, then verify the mole form.
Check the model response
V = NkT/p = 1.66 × 10⁻³ m³. N/Nₐ = 0.0500 mol, and nRT/p gives the same volume because R = Nₐk.
guided practice
4. Guided practice
Use each hint only to choose the governing definition, equation or sign convention.
Ideal-gas equations, particles and moles 12(c)–(d)
Question 1
At constant volume, an ideal gas changes from 1.2 × 10⁵ Pa at 300 K to 450 K. Find its new pressure.
Hint: Start with pV = NkT and identify what remains fixed.
Check the model response
For fixed N and V, p/T is constant. p₂ = 1.2 × 10⁵(450/300) = 1.8 × 10⁵ Pa.
independent practice
5. Independent practice
Solve without repair notes and state every idealisation, system boundary and sign convention used.
Ideal-gas equations, particles and moles 12(c)–(d)
Question 1
A 2.00 mol ideal gas at 350 K occupies 0.0400 m³. Find pressure and show how N, n, k, R and Nₐ are related.
Check the model response
p = nRT/V = 1.45 × 10⁵ Pa. N = nNₐ and R = Nₐk, so Nk = nNₐk = nR.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Ideal-gas equations, particles and moles 12(c)–(d)
Question 1
Use pV = NkT to find N for p = 2.0 × 10⁵ Pa, V = 3.0 × 10⁻³ m³ and T = 290 K; then find n.
Check the model response
N = pV/(kT) = 1.50 × 10²³ molecules. With Nₐ = 6.02 × 10²³ mol⁻¹, n = 0.249 mol.
Re-test practice
7. Delayed re-test practice
Return after at least three days and solve these fresh contexts without reopening earlier responses. The recorded plan enforces the delay and uses a separate re-test family for selected-response skill-group evidence.
Ideal-gas equations, particles and moles 12(c)–(d)
Question 1
A fixed amount of ideal gas doubles both its kelvin temperature and volume. State the pressure factor.
Check the model response
From pV = NkT, p ∝ T/V. Both numerator and denominator double, so pressure is unchanged.