Heat Engines and Efficiency
For a cyclic heat engine absorbing magnitude Q_H from a hot reservoir and rejecting magnitude Q_C to a cold reservoir, W = Q_H − Q_C and η = W/Q_H = 1 − Q_C/Q_H, with 0 ≤ η < 1.
Why this shows up in the exam
Finding work from heat flows · Efficiency of a specified gas cycle · Comparing actual engines with reversible limits
Learn the idea
A heat engine converts only part of absorbed heat into cyclic work and rejects the rest. Because the working substance returns to its initial state each cycle, its net work is the difference between heat received and heat rejected.
🧠 Memory hook: Input heat splits into work plus rejected heat.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- W = Q_H - Q_C — cycle energy balance using positive heat magnitudes
- η = W/Q_H = 1 - Q_C/Q_H — thermal efficiency of any heat engine
How to approach it
- 1Draw heat-in, work-out, and heat-out arrows
- 2Use the cycle energy balance
- 3Compare the result with the Carnot upper bound when temperatures are given
Common slip-ups that cost marks
- •Dividing work by rejected heat
- •Treating signed Q_C as a positive term without changing formula
- •Claiming complete conversion of cyclic heat into work
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A gas absorbs 500 J of heat and does 200 J of work. What is the change in its internal energy?
More from Thermodynamics
Thermodynamic Processes and P-V Diagrams
Study different thermodynamic processes (isothermal, isobaric, isochoric, adiabatic, polytropic, cyclic), their definitions, characteristics, and graphical representation on P-V diagrams.
Laws of Thermodynamics
Understand the zeroth and first laws of thermodynamics, including their statements, implications, and applications to physical systems.
Internal Energy, Heat, and Work
Explore the concepts of internal energy, heat, and work, including their definitions, relationships, and how they change during various thermodynamic processes.
Ideal Gas Law and Equation
Learn the ideal gas equation, its relation to physical quantities like pressure, volume, temperature, and density, and its use in describing the behavior of ideal gases.
Gibbs Free Energy and Spontaneity
Learn how Gibbs free energy determines spontaneity, how to calculate it, and its dependence on temperature, pressure, and other thermodynamic parameters.
Entropy and Its Changes
Understand entropy as a measure of disorder, how it changes in physical and chemical processes, and its calculation in various scenarios including phase transitions and isothermal processes.