Unit 21: The Second Law of Thermodynamics
Why heat engines can't be perfectly efficient, and the entropy that gives time itself a direction.
6 topics · 21 questions
Each topic is a path, not a menu: work down it in order and every question builds on the one above. Click any of them to watch the answer draw itself.
Heat Engines
- How it worksHow does a heat engine's efficiency come from the fraction of absorbed heat converted into work each cycle?
- Worked exampleFind the efficiency of a heat engine that absorbs 2000 J of heat and performs 500 J of work per cycle.
- Common mistakeWhy doesn't a more powerful engine necessarily mean a more efficient one?
Your turn1 of 2
A heat engine absorbs 2393 J of heat and performs 619 J of work per cycle. What is its efficiency (as a fraction)?The Carnot Cycle
- How it worksHow do the four reversible steps of a Carnot cycle trace out a specific path on a PV diagram?
- Worked exampleFind the maximum possible efficiency of a heat engine operating between 600 K and 300 K reservoirs.
- Common mistakeWhy doesn't a Carnot engine reach 100 percent efficiency even in a perfectly frictionless, idealized world?
- Going furtherWhat happens to a Carnot engine's maximum efficiency as its cold reservoir's temperature approaches absolute zero?
Your turn1 of 2
A heat engine operates between a hot reservoir at 709 K and a cold reservoir at 330 K. What is the maximum possible efficiency it could achieve?Statements of the Second Law
- How it worksHow do the Kelvin and Clausius statements of the second law describe the same forbidden process from two directions?
- Common mistakeWhy doesn't the second law of thermodynamics forbid a refrigerator from moving heat from cold to hot?
- Going furtherWhat happens to a proposed engine design the moment it's shown to violate the second law?
Your turn1 of 2
A refrigerator moves heat from its cold interior to the warmer room outside, which sounds like the 'wrong direction' the second law says heat can't spontaneously flow. Why is this not a violation?Refrigerators and Heat Pumps
- How it worksHow does a refrigerator use work input to pump heat from a cold interior out into a warmer room?
- Worked exampleFind the coefficient of performance of a refrigerator that removes 300 J of heat from its interior using 100 J of work.
- Common mistakeWhy doesn't a refrigerator actually create cold, rather than just relocating heat somewhere else?
- Going furtherWhat happens to a heat pump's coefficient of performance as the temperature difference it works across grows larger?
Your turn1 of 2
A refrigerator removes heat Qc from its interior using work W. Write an expression, in terms of Qc and W, for its coefficient of performance.Entropy
- How it worksHow does entropy measure the number of microscopic arrangements consistent with a system's observable state?
- Worked exampleFind the change in entropy when 1000 J of heat flows into a reservoir held at a constant 250 K.
- Common mistakeWhy isn't entropy the same thing as simple disorder in the everyday, messy-room sense of the word?
Your turn1 of 2
1454 J of heat flows into a reservoir held at a constant 295 K. What is the change in entropy, in joules per Kelvin?Entropy and the Arrow of Time
- How it worksHow does the second law's requirement that total entropy never decreases give time a preferred direction?
- Common mistakeWhy doesn't the second law forbid entropy from ever decreasing anywhere, including some small local region?
- Going furtherWhat happens to the total entropy of the universe as more and more energy spreads out into unusable, low-grade heat?
- Ties togetherHow does the statistical definition of entropy connect microscopic randomness to the macroscopic heat engines you just studied?
Your turn1 of 2
A refrigerator's interior becomes more ordered (lower entropy) as it cools down. Does this local entropy decrease violate the second law of thermodynamics?