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.
Specific heat capacity and specific latent heat 13(g)
Question 1
Define specific heat capacity and specific latent heat. Find the energy to heat 0.40 kg of water by 15 K and then vaporise 0.050 kg if c = 4200 J kg⁻¹ K⁻¹ and L = 2.26 × 10⁶ J kg⁻¹.
Check the model response
Specific heat capacity is energy per unit mass per kelvin; specific latent heat is energy per unit mass for a phase change without temperature change. Q = mcΔT = 25.2 kJ and Q = mL = 113 kJ.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Specific heat capacity and specific latent heat 13(g)
Check this idea
Misconception: Specific heat capacity describes the whole object.
Repair: Heat capacity is for a whole object; specific heat capacity is per unit mass per kelvin.
Check this idea
Misconception: Latent heating increases temperature throughout a phase change.
Repair: During a constant-temperature phase change, energy changes microscopic potential energy rather than mean kinetic energy.
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.
Specific heat capacity and specific latent heat 13(g)
Model 1
A 0.20 kg metal at 200 °C is placed in 0.50 kg water at 20 °C. The final temperature is 30 °C; neglect losses and use cwater = 4200 J kg⁻¹ K⁻¹. Find the metal's specific heat capacity.
Check the model response
Energy gained by water is 0.50(4200)(10) = 21,000 J. The metal loses 0.20c(170), so c = 21,000/[0.20(170)] = 618 J kg⁻¹ K⁻¹.
guided practice
4. Guided practice
Use each hint only to choose the governing definition, equation or sign convention.
Specific heat capacity and specific latent heat 13(g)
Question 1
A 0.080 kg ice sample melts at constant temperature using 26.7 kJ. Find its specific latent heat and state which microscopic energy changes.
Hint: Use Q = mL and distinguish kinetic from potential energy.
Check the model response
L = Q/m = 26,700/0.080 = 3.34 × 10⁵ J kg⁻¹. Mean kinetic energy and temperature remain constant; microscopic potential energy increases as the structure changes.
independent practice
5. Independent practice
Solve without repair notes and state every idealisation, system boundary and sign convention used.
Specific heat capacity and specific latent heat 13(g)
Question 1
A heater supplies 36 kJ to 0.60 kg of liquid, raising it by 20 K. A further 90 kJ boils 0.040 kg. Find c and L.
Check the model response
c = 36,000/[0.60(20)] = 3.0 × 10³ J kg⁻¹ K⁻¹. L = 90,000/0.040 = 2.25 × 10⁶ J kg⁻¹.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Specific heat capacity and specific latent heat 13(g)
Question 1
Define c and L with units, and explain the microscopic difference between warming and melting.
Check the model response
c is energy per unit mass per kelvin, J kg⁻¹ K⁻¹. L is phase-change energy per unit mass, J kg⁻¹. Warming raises mean kinetic energy; melting at constant temperature primarily raises microscopic potential energy.
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.
Specific heat capacity and specific latent heat 13(g)
Question 1
Why does a temperature plateau during boiling not imply that no energy is transferred?
Check the model response
Energy is still supplied as mL. It changes microscopic potential energy and phase rather than mean kinetic energy, so thermodynamic temperature remains constant during the phase change.