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.
Work, zeroth law and first law 13(d)–(f)
Question 1
A gas expands by 1.50 × 10⁻³ m³ against 2.00 × 10⁵ Pa while receiving 500 J by heating. Find work by the gas, work on the gas and ΔU using ΔU = Q + W.
Check the model response
Work by gas = pΔV = 300 J. Work on gas W = −300 J, so ΔU = 500 − 300 = +200 J. The sign of W must follow the stated first-law convention.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Work, zeroth law and first law 13(d)–(f)
Check this idea
Misconception: Work by and work on the gas have the same sign.
Repair: They have opposite signs. In ΔU = Q + W, W is work done on the system.
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.
Work, zeroth law and first law 13(d)–(f)
Model 1
A gas is compressed by 2.0 × 10⁻⁴ m³ at constant external pressure 3.0 × 10⁵ Pa while 25 J leaves by heating. Find ΔU with ΔU = Q + W.
Check the model response
ΔV = −2.0 × 10⁻⁴ m³. Work by gas is pΔV = −60 J, so work on gas W = +60 J. Q = −25 J, hence ΔU = −25 + 60 = +35 J.
guided practice
4. Guided practice
Use each hint only to choose the governing definition, equation or sign convention.
Work, zeroth law and first law 13(d)–(f)
Question 1
State the zeroth law and explain how it justifies a thermometer.
Hint: Use three systems and the transitive equilibrium relation.
Check the model response
If A and B are each in thermal equilibrium with C, A and B are in thermal equilibrium with each other. A thermometer is C: equal readings correspond to a shared temperature and therefore mutual thermal equilibrium.
independent practice
5. Independent practice
Solve without repair notes and state every idealisation, system boundary and sign convention used.
Work, zeroth law and first law 13(d)–(f)
Question 1
For each of expansion and compression, relate the signs of pΔV, work by the gas, work on the gas and the W in ΔU = Q + W.
Check the model response
Expansion has ΔV > 0 and work by gas +pΔV, so work on gas and W are negative. Compression has ΔV < 0 and work by gas negative, so work on gas and W are positive.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Work, zeroth law and first law 13(d)–(f)
Question 1
A gas receives 260 J by heating and does 90 J of work. Use the syllabus convention to find ΔU and state the zeroth law.
Check the model response
Work on the gas is W = −90 J, so ΔU = Q + W = 170 J. If two systems are each in thermal equilibrium with a third, they are in thermal equilibrium with each other.
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.
Work, zeroth law and first law 13(d)–(f)
Question 1
A gas loses 40 J by heating while 75 J of work is done on it. Find ΔU.
Check the model response
Q = −40 J and W = +75 J in ΔU = Q + W, so ΔU = +35 J.