Thermodynamics & Energy · AP Physics 2 Unit 2
Carnot Cycle & Heat Engine Efficiency Simulator
Key exam takeaway: No heat engine operating between two temperatures can exceed the Carnot efficiency η = 1 - Tc/Th. Heat rejection to a cold reservoir is unavoidable by the 2nd Law.
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3D Simulation Stage● 60 FPS
Parameter Controls
K
K
J
Live Derivations & Metrics
Carnot Ceiling Efficiency
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Max Net Work Output
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Rejected Waste Heat Qc
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Total Cyclic Entropy ΔS
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: Heat engine operates between 600K and 300K absorbing 1200J. Find max efficiency, max work output, and min rejected heat.
Step-by-Step Derivation:
- η = 1 - 300/600 = 50%. Max work W = 1200 * 0.5 = 600J. Minimum rejected heat Qc = 600J.
Worked Problem
Problem: What is a perpetual motion machine of the second kind? Why is it impossible despite conserving energy?
Step-by-Step Derivation:
- Extracts heat from a single reservoir to produce work without heat rejection. Though conserving energy, it violates the 2nd Law (Kelvin statement); cold reservoir rejection is mandatory.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: State Clausius and Kelvin statements of the 2nd Law of Thermodynamics. Are they equivalent?
Answer Key: Clausius: Heat cannot spontaneously flow from cold to hot. Kelvin: Cannot convert 100% heat to work from a single reservoir. They are strictly equivalent.
Q2. Variant 2: What is Entropy? What arrow of time does the entropy increase principle define for isolated systems?
Answer Key: Entropy measures microstate disorder. In isolated systems, total entropy never decreases (ΔS ≥ 0), dictating the irreversible thermodynamic arrow of time toward disorder.
Q3. Variant 3: A kitchen refrigerator pumps heat from -18°C freezer to 25°C room air. Does this violate the 2nd Law?
Answer Key: Not at all! The 2nd Law forbids SPONTANEOUS reverse heat flow. Refrigerators consume external electrical compressor work to force heat uphill.
Frequently Asked Questions & Misconceptions
Why do coal/nuclear power plants require gargantuan hyperbola cooling towers?
By Carnot's theorem and 2nd Law, exhaust steam must reject waste heat to a cold reservoir to condense back to water before re-entering boilers.
Why can't we collect 100% of car exhaust waste heat to power a secondary engine with "zero waste"?
Any secondary heat recovery engine is bound by the same Carnot limit between exhaust temp and ambient air, requiring unavoidable waste rejection.
If a refrigerator door is left wide open in a sealed insulated room, does room temperature rise or fall?
Rises! Refrigerator exhausts heat Q_out = Q_in + W_electric. With door open, heat absorbed equals heat released, plus the motor's electrical energy turns to room heat.
Does life violate the 2nd Law of Thermodynamics by creating biological order out of disorder?
No! Living organisms are open non-equilibrium systems. They maintain internal low entropy by consuming food and dumping vastly greater entropy into the environment.