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.
Internal energy, temperature and thermal equilibrium 13(a)–(c)
Question 1
Distinguish internal energy, thermodynamic temperature and heating, then state when two systems reach thermal equilibrium.
Check the model response
Internal energy is the sum of random microscopic kinetic and potential energies. Thermodynamic temperature is proportional to mean microscopic kinetic energy. Heating is energy transfer caused by a temperature difference; it proceeds from higher to lower temperature until both temperatures are equal and there is no net transfer.
repair
2. Repair the common breaks
Use only the correction matching an error, then retry the corresponding diagnostic.
Internal energy, temperature and thermal equilibrium 13(a)–(c)
Check this idea
Misconception: Heat is energy stored inside a hot body.
Repair: Internal energy is the store; heating is energy transferred because of a temperature difference.
Check this idea
Misconception: Equal temperature means equal internal energy.
Repair: Equal temperature means equal mean microscopic kinetic energy, not equal total internal 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.
Internal energy, temperature and thermal equilibrium 13(a)–(c)
Model 1
Two copper blocks of unequal mass begin at the same temperature. Compare their mean microscopic kinetic energy, internal energy and net heating when placed in contact.
Check the model response
Their equal thermodynamic temperatures imply equal mean microscopic kinetic energy per particle. The larger block can have greater total internal energy because it contains more particles. Since temperatures are equal, they are in thermal equilibrium and there is no net heating.
guided practice
4. Guided practice
Use each hint only to choose the governing definition, equation or sign convention.
Internal energy, temperature and thermal equilibrium 13(a)–(c)
Question 1
A hot small object and a cooler large object touch. Predict the direction and stopping condition for heating without comparing their total internal energies.
Hint: Temperature, not total internal energy, fixes the direction.
Check the model response
Net heating is from the higher-temperature small object to the lower-temperature large object until their temperatures are equal. Equal internal energies are neither required nor generally produced.
independent practice
5. Independent practice
Solve without repair notes and state every idealisation, system boundary and sign convention used.
Internal energy, temperature and thermal equilibrium 13(a)–(c)
Question 1
Explain why equal-temperature samples can have different internal energies and why energy can still transfer without being stored as 'heat'.
Check the model response
Temperature concerns mean microscopic kinetic energy, while internal energy totals microscopic kinetic and potential energies over all particles. Different masses, phases or interactions therefore change U. Heat is not a store; heating is energy crossing a boundary because of a temperature difference.
Practice exit check
6. Practice assessment
Use this as extra closed-book practice, then complete the separate recorded assessment in your plan.
Internal energy, temperature and thermal equilibrium 13(a)–(c)
Question 1
Define internal energy and thermal equilibrium, and connect thermodynamic temperature to molecular motion.
Check the model response
U is the sum of random microscopic kinetic and potential energies. T is proportional to mean microscopic kinetic energy. Thermal equilibrium means equal temperature and no net heating between systems in thermal contact.
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.
Internal energy, temperature and thermal equilibrium 13(a)–(c)
Question 1
Two objects have equal internal energy but different temperatures. Can they be in thermal equilibrium? Explain.
Check the model response
Not necessarily. Equilibrium requires equal temperature, not equal total internal energy; if their temperatures differ, net heating occurs when they are placed in thermal contact.