AP® Chemistry review sheet from Aim for Five (aimforfive.com/chem/units/6/6-3)
Unit 6 · Topic 6.3
6.3 Heat Transfer and Thermal Equilibrium
Heat flows from a warmer object to a cooler one because faster-moving particles bump into slower ones and pass along some of their energy. The flow stops at thermal equilibrium, when both objects have the same average kinetic energy and so the same temperature.
Key terms
- temperature
- average kinetic energy
- heat transfer
- thermal equilibrium
Temperature is average kinetic energy
The particles in any substance are always moving. Temperature measures the average kinetic energy of those particles (on the Kelvin scale, the two are directly proportional; see topic 3.5). In a warmer object, the particles are moving faster on average.
On average is important. Even in a cold object some particles are fast, and even in a hot object some are slow. Temperature describes the average, not every particle.
How collisions move energy
When two objects touch, particles at the boundary collide. When a fast particle from the warm object hits a slower particle from the cool object, the fast one usually slows down and the slow one speeds up. Energy has been transferred.
Collisions happen in both directions, but because the warm object's particles are faster on average, more energy goes from warm to cool than from cool to warm. The net flow is always from the higher temperature to the lower temperature. This energy transfer is called heat transfer or heat exchange.
As the warm object loses energy, its particles slow down and its temperature drops. As the cool object gains energy, its particles speed up and its temperature rises.
Thermal equilibrium
Eventually both objects reach the same temperature. Now their particles have the same average kinetic energy. Collisions still happen and individual particles still swap energy, but the gains and losses balance, so there is no net flow of energy. This is thermal equilibrium.
The final temperature is always between the two starting temperatures. It sits closer to the starting temperature of whichever object has the larger heat capacity (more mass, or a higher specific heat). A large lake barely warms when you drop a hot rock in it.
Bookkeeping the energy
If the two objects are insulated from everything else, the energy lost by the warm object equals the energy gained by the cool one. In symbols, q(warm) + q(cool) = 0, or −q(warm) = q(cool). Each q is calculated with q = mcΔT (topic 6.4).
This lets you predict a final temperature or work out an unknown specific heat from a mixing experiment.
Heat is not the same as temperature
A bathtub of warm water holds far more thermal energy than a cup of boiling water, because it has so many more particles. Yet the cup has the higher temperature. If you poured the cup into the tub, energy would flow from the cup's water to the tub's water, because direction depends on temperature, not on total energy.
Worked examples
Try each one yourself first, then open the solution.
- Example 1Calculator allowed
Finding a final temperature
A 50.0 g piece of iron at 95.0 °C is dropped into 100.0 g of water at 22.0 °C in an insulated cup. The specific heat of iron is 0.449 J/(g·°C) and of water is 4.18 J/(g·°C). What is the final temperature, assuming no energy is lost?
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- Step 1: Energy lost by the iron = energy gained by the water, so −q(iron) = q(water).
- Step 2: Write each q with q = mcΔT, where ΔT = T(final) − T(initial): −(50.0)(0.449)(Tf − 95.0) = (100.0)(4.18)(Tf − 22.0).
- Step 3: Simplify: 22.45(95.0 − Tf) = 418(Tf − 22.0), so 2132.75 − 22.45Tf = 418Tf − 9196.
- Step 4: Collect terms: 2132.75 + 9196 = 418Tf + 22.45Tf, so 11328.75 = 440.45Tf and Tf = 25.7 °C.
- Step 5: Sanity check: the final temperature is between 22.0 and 95.0 °C, and much closer to the water's starting temperature because the water has a much larger heat capacity (418 J/°C versus 22.45 J/°C). The iron gave about 1.56 × 10³ J to the water.
Answer: Tf ≈ 25.7 °C
- Example 2
Trap: explaining at the particle level
Two identical 100 g copper blocks, one at 20 °C and one at 60 °C, are pressed together and insulated. A student says the energy flow stops at 40 °C because 'the particles stop colliding.' Predict the final temperature and correct the explanation.
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- Step 1: The blocks have the same mass and the same specific heat, so whatever energy one loses, the other gains with the same size temperature change. The final temperature is the average: 40 °C.
- Step 2: Before equilibrium, particles in the 60 °C block have a higher average kinetic energy. In collisions at the boundary, energy is transferred, on balance, from the faster particles to the slower ones.
- Step 3: At 40 °C both blocks have the same average kinetic energy. The particles keep moving and colliding, but energy transfers in each direction now balance, so there is no net heat flow.
Answer: Final temperature 40 °C. Collisions never stop; at thermal equilibrium they simply transfer no net energy because both blocks have the same average kinetic energy.
Common mistakes
- Assuming the final temperature is the average of the two starting temperatures. That's only true when the two objects have equal heat capacities (same m × c).
- Saying particles stop moving or stop colliding at thermal equilibrium. Motion continues; only the net transfer stops.
- Treating heat and temperature as the same thing. Temperature is an average property; heat is energy that moves.
- Writing the energy balance as q(warm) = q(cool) without a minus sign, which gives a final temperature outside the starting range.
On the exam
- Explanations that earn credit tie the macroscopic observation (temperatures become equal) to the particle level (collisions transfer kinetic energy until the average kinetic energies match).
- Mixing problems may ask for a final temperature or an unknown specific heat. Check that your final temperature lies between the starting values.
Connected topics
Videos
Check yourself
4 questions on 6.3 Heat Transfer and Thermal Equilibrium. Pick an answer to see if you got it, and why.
A hot iron block is placed in a cup of cool water. Which of the following is true once the block and the water reach thermal equilibrium?
Two samples of the same gas are separated by a thin metal wall. Sample 1 is at 300 K and sample 2 is at 400 K. Which of the following best describes how energy is transferred between them?
A 100.0 g block of aluminum (c = 0.897 J/(g·°C)) and a 100.0 g block of copper (c = 0.385 J/(g·°C)) are both heated to 90.0 °C. Each is dropped into its own insulated cup containing 200.0 g of water at 20.0 °C. Which cup reaches the higher final temperature, and why?
50.0 g of water at 80.0 °C is mixed with 150.0 g of water at 20.0 °C in an insulated container. What is the final temperature of the mixture?
0 of 4 answered