Heat and WorkTemperature and EntropyEngines and Refrigerators
Thermodynamics is the science of energy moving through matter. It explains why engines can do work, why refrigerators need power, why hot coffee cools down, and why no machine can turn every bit of heat into useful motion.
The Big Idea
Temperature tells us the average motion of particles. Heat is energy transferred because of a temperature difference. Work is energy transferred by organized pushes, pulls, compression, or expansion. Thermodynamics connects all three.
ΔU = Q - WΔU is change in internal energy, Q is heat added to the system, and W is work done by the system.
If heat enters a gas and the gas expands to push a piston, some energy stays as particle motion and some leaves as useful work. That accounting rule is the first law.
Feynman's Shortcut: Skip the Hidden Machinery
Feynman's thermodynamics lecture begins with a surprising example: stretch a rubber band and it warms; let it relax quickly and it cools. Heat the stretched band and it pulls harder. The molecular details are tangled, but thermodynamics can still predict relationships between heat, work, temperature, and force.
Rubber band engine
Heating one side of a wheel made of rubber-band spokes makes those bands contract more strongly. The imbalance can turn the wheel, even though the engine is wonderfully inefficient.
The lesson
Thermodynamics is powerful because it constrains what any material can do. Rubber, steam, alcohol, or gas may have different internal stories, but no cyclic engine can beat the same reversible limit.
Interactive Heat Engine
Use the controls to change the hot reservoir, cold reservoir, and working gas. The simulator shows particle speed, heat flow, work output, rejected heat, and the theoretical Carnot efficiency limit.
Efficiency0%
Work Output0 J
Heat Rejected0 J
Particle Energy0%
Heat flows from the hot side into the working gas. Some becomes work; the rest must be rejected to the cold side.
The Four Laws
Zeroth Law: temperature can be compared
If A is in thermal equilibrium with B, and B with C, then A and C are also in equilibrium. This makes thermometers possible.
First Law: energy is conserved
Energy changes form, but the total bookkeeping still balances: heat in can become internal energy, work, or both.
Second Law: entropy tends to increase
Heat naturally spreads from hot to cold. Perfectly converting heat into work is impossible because some energy becomes unavailable.
Third Law: absolute zero is unreachable
As temperature approaches 0 K, a perfect crystal approaches minimum entropy. Real processes cannot reach absolute zero in finite steps.
How a Heat Engine Works
1
Absorb heat from a hot reservoirFuel, sunlight, steam, or combustion raises the energy of the working fluid.
2
Convert some heat into workThe working fluid expands, spins a turbine, pushes a piston, or drives another mechanical load.
3
Reject waste heat to a cold reservoirThe engine must dump some energy so the cycle can reset and run again.
4
Repeat the cycleReal engines lose extra energy to friction, turbulence, sound, exhaust, and imperfect heat transfer.
Carnot's Limit
A reversible engine is the ideal engine: no friction, no turbulence, and no heat transfer across a large temperature jump. Each step can be reversed by an infinitesimal change. Feynman emphasizes that this ideal is not mainly about building a perfect machine; it is a measuring stick for every possible machine.
Qhot / Thot = Qcold / TcoldFor a reversible cycle, the heat exchanged at each reservoir balances when divided by absolute temperature. That is the doorway to entropy.
Because W = Qhot - Qcold, the best possible efficiency is 1 - Tcold/Thot. A colder cold side or hotter hot side raises the ceiling, but reaching 100% would require a cold reservoir at absolute zero.
Practice Problems
Easy1. A system absorbs 120 J of heat and does 45 J of work. What is ΔU?
Hint: ΔU = Q - W = 120 - 45 = 75 J.
Medium2. A heat engine absorbs 500 J and outputs 150 J of work. What is its efficiency as a percent?