Thermodynamics tracks how energy moves as heat and work, and it explains why heat flows spontaneously from hot to cold. After this unit you should be able to apply to a gas, explain what entropy measures, and calculate the efficiency of an engine or the performance of a refrigerator or heat pump.
Read the overview first to see how the four laws connect, then work through each topic's notes and try the checkpoint question before checking the answer.
This unit takes the energy conservation you learned in mechanics and extends it to heat and to the internal energy of particles. It then asks a new question that energy conservation alone can't answer: which processes actually happen on their own?
Honors Physics Unit 12 covers thermodynamics in four parts. You start with thermal equilibrium and the zeroth law, which explain what temperature is and why thermometers work. Then you apply the first law, , to gases, using the ideal gas law and PV diagrams to find work. Next comes the second law and entropy, including for reversible heat transfer at constant temperature and why heat flows from hot to cold. The unit ends with heat engines, heat pumps, and refrigerators, where you calculate efficiency, Carnot efficiency, and coefficient of performance (COP).
Heat moves from the hotter object to the cooler one until both reach the same temperature, which is thermal equilibrium. The zeroth law says that if A and B each match a thermometer C, then A and B match each other. That is the whole reason a thermometer gives meaningful readings.
The first law, , is energy conservation for thermal systems. Heat added raises internal energy, and work the gas does on its surroundings lowers it. For an ideal gas, internal energy depends only on temperature, so constant temperature means .
The second law says the total entropy of an isolated system never decreases. An engine has to dump some heat into a cold reservoir to keep total entropy from dropping. That is why real engines are well below 100% efficient and why the Carnot efficiency sets the ceiling.
The first law says you never lose energy, and the second law says energy tends to spread out into less useful forms. The first law tells you how much energy goes where, and the second tells you which processes are possible.
Two objects are in thermal equilibrium when they are at the same temperature, so no net heat flows between them.
The first law is energy conservation for systems that exchange heat and work.
The second law says the total entropy of an isolated system never decreases.
A heat engine takes in heat Q_H from a hot reservoir, does work W, and rejects heat Q_C to a cold reservoir.
Two objects are in thermal equilibrium when they are at the same temperature, so no net heat flows between them. If they start at different temperatures, heat flows from the hotter object to the cooler one until the temperatures match. A cup of 80°C coffee left on a 20°C desk cools until it reaches room temperature, and then it stops changing.
The zeroth law states that if system A is in thermal equilibrium with system C, and B is also in thermal equilibrium with C, then A and B are in thermal equilibrium with each other. This sounds obvious, but it is what makes temperature a real, measurable property. A thermometer is system C. You let it reach equilibrium with one object, read it, then do the same with a second object. Matching readings mean the two objects are at the same temperature even though they never touched.
A common confusion is mixing up heat and temperature. For an ideal gas, temperature is proportional to the average translational kinetic energy of its particles. Heat is energy in transit because of a temperature difference. A bathtub of 40°C water holds far more thermal energy than a 90°C cup of tea, yet heat would still flow from the tea to the bath.
In thermodynamics, use kelvin. The conversion is , so 20°C is about 293 K.
Check yourself. A metal spoon and a wooden spoon have both sat in a 22°C kitchen for an hour. The metal one feels colder. Which one is at a lower temperature? (Answer: Neither. Both are in thermal equilibrium with the room at 22°C. The metal feels colder because it conducts heat away from your hand faster.)
The first law is energy conservation for systems that exchange heat and work. In this guide it is written as . Here is the change in internal energy, is heat added to the system, and is work done by the system. Some textbooks, including AP Physics 1, write and define as work done on the gas. Both versions describe the same physics, so check which one your class uses.
Pressure-volume work comes from a gas changing volume. For a slow process at constant pressure, . On a PV diagram, the work done by the gas is the signed area under the process curve: it is positive for expansion and negative for compression. Different paths between the same states can give different amounts of work. In a rigid container, , so pressure-volume work is zero. Other kinds of work, such as work done by a stirring paddle, can still occur.
The ideal gas law, , links the state of the gas. Because an ideal gas's internal energy depends only on temperature, an isothermal process has .
Worked example. An ideal gas absorbs 500 J of heat and expands slowly at a constant pressure of Pa from m³ to m³. The work done by the gas is J. Then J, so the gas's internal energy rises by 400 J and its temperature goes up.
Check yourself. A gas in a sealed rigid tank absorbs 300 J of heat, and no other work is done on or by the gas. What is ? (Answer: The volume can't change, so pressure-volume work is zero. With no other work, J.)
| Process | What stays constant | Work done by gas | First law becomes |
|---|---|---|---|
| Isothermal (ideal gas) | Temperature | Equal to Q | $\Delta U = 0$, so $Q = W$ |
| Isobaric | Pressure | $W = P\Delta V$ | $\Delta U = Q - P\Delta V$ |
| Isochoric (isovolumetric) | Volume | $W = 0$ | $\Delta U = Q$ |
| Adiabatic | No heat flow ($Q = 0$) | Equal to $-\Delta U$ | $\Delta U = -W$ |
The second law says the total entropy of an isolated system never decreases. In everyday terms, heat flows on its own from hot to cold, never the reverse. Energy conservation alone would allow a cold drink to get colder while the room gets warmer, but that never happens because it would lower total entropy.
Entropy () is often called disorder. A more precise picture is that entropy measures how spread out energy is, or how many microscopic arrangements (microstates) fit the same overall state. A gas filling a room has many more possible arrangements than the same gas squeezed into a corner, so it has higher entropy.
For a reversible heat transfer at constant absolute temperature , the entropy change is , in J/K. Reversible heat added gives positive , and reversible heat removed gives negative .
Worked example. 1200 J of heat flows from a reservoir held at 400 K to one held at 300 K. The hot object loses entropy: J/K. The cold object gains entropy: J/K. The total is J/K. Because the same heat divided by a smaller temperature gives a bigger number, heat flowing from hot to cold always raises total entropy.
Entropy can decrease locally, like water freezing in a freezer, as long as the surroundings gain more.
Check yourself. 668 J of heat melts 2.0 g of ice at 273 K. What is the ice's entropy change? (Answer: J/K, positive because the ice gains heat.)
A heat engine takes in heat from a hot reservoir, does work , and rejects heat to a cold reservoir. Over a full cycle , so . Efficiency is . The second law forbids , so no engine reaches 100%. The best possible engine between two temperatures is a Carnot engine, with in kelvin.
Refrigerators and heat pumps run the cycle backward. Work input moves heat from cold to hot. Their performance is measured by the coefficient of performance (COP). A refrigerator cares about heat removed, so . A heat pump cares about heat delivered, so . COP is often 3 or more, which doesn't break energy conservation because the device moves heat rather than creating it.
Worked example. An engine absorbs 2000 J per cycle and rejects 1500 J. The work is J, so , or 25%. If it runs between 600 K and 300 K, the Carnot limit is . The 25% engine is possible because it's below that ceiling. A claim of 60% between those same temperatures would be impossible.
Check yourself. A heat pump uses 1000 J of work to deliver 4000 J of heat into a house. What is its heating COP, and how much heat did it pull from outside? (Answer: , and J came from outside.)
| Device | Direction of heat flow | Goal | Performance measure |
|---|---|---|---|
| Heat engine | Hot to cold, producing work | Get work out | $e = W/Q_H$, always less than 1 |
| Refrigerator or air conditioner | Cold to hot, using work | Remove heat from the cold side | $COP = Q_C/W$, can exceed 1 |
| Heat pump | Cold to hot, using work | Deliver heat to the warm side | $COP = Q_H/W$, always greater than 1 |
| Term | Definition |
|---|---|
| Thermal equilibrium | The condition where objects in contact have the same temperature and no net heat flows between them. |
| Zeroth law of thermodynamics | Two systems each in thermal equilibrium with a third are in thermal equilibrium with each other, which is why thermometers work. |
| Internal energy | The total kinetic and potential energy of a system's particles, which for an ideal gas depends only on temperature. |
| First law of thermodynamics | Energy conservation for thermal systems, written $\Delta U = Q - W$ when $W$ is work done by the system. |
| PV diagram | A graph of pressure versus volume. The signed area under a process curve gives the work done by the gas, positive for expansion and negative for compression. |
| Entropy | A measure of how spread out a system's energy is, with $\Delta S = Q_{rev}/T$ for reversible heat transfer at constant absolute temperature. |
| Second law of thermodynamics | The total entropy of an isolated system never decreases, so heat flows spontaneously only from hot to cold. |
| Heat engine | A device that takes heat from a hot reservoir, converts part of it to work, and rejects the rest to a cold reservoir. |
| Carnot efficiency | The highest efficiency any engine can reach between two reservoirs, $1 - T_C/T_H$ with temperatures in kelvin. |
| Coefficient of performance | For a refrigerator or heat pump, the useful heat moved divided by the work input, a value that is often greater than 1. |
Formulas like , , and all need absolute temperature. The Carnot efficiency between 100°C and 20°C is not . Convert to 373 K and 293 K first, which gives a maximum efficiency of about 21%.
This happens because textbooks use two conventions. With , is work done by the gas, so expansion gives positive . With , is work done on the gas, so expansion gives negative . Pick your class's version and check the sign by asking whether the gas expanded or got compressed.
Temperature is a property of an object, while heat is energy moving between objects. A large lukewarm object can hold more thermal energy than a small hot one. Heat flow depends on the temperature difference, not on which object has more total energy.
The second law is about total entropy of an isolated system. A refrigerator lowers the entropy of the food inside, which is allowed because it releases even more entropy into the kitchen. Always add up the entropy changes of the system and its surroundings before deciding if a process breaks the law.