Thermodynamics & Energy · AP Physics 2
Joule's Mechanical Equivalent of Heat Simulator
Key exam takeaway: Joule's paddle wheel experiment proved mechanical work and heat are interchangeable forms of energy, establishing the 1st Law of Thermodynamics (1 cal = 4.186 J).
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Live Derivations & Metrics
Total Mechanical Work W
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Equivalent Heat in Calories
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Water Temperature Rise Δt
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Measured Heat Equivalent J
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: Water drops 50m over a waterfall. If all potential energy converts to internal energy, find water temp rise.
Step-by-Step Derivation:
- mgh = c*m*Δt => Δt = gh/c = 10*50 / 4200 ≈ 0.119°C.
Worked Problem
Problem: What is the historic significance of Joule's heat equivalent experiment? What theory did it overturn?
Step-by-Step Derivation:
- Overturned the dominant caloric fluid theory, proving heat is a form of molecular kinetic energy, establishing the 1st Law.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: Why did Joule enclose the paddle-wheel in an insulated double-walled calorimeter?
Answer Key: To eliminate parasitic heat conduction, convection, and radiation leaks to ambient air, ensuring all mechanical work converts into water heat.
Q2. Variant 2: If the falling mass impacts the floor with residual kinetic energy, does measured J err high or low?
Answer Key: Err high! Uncaptured kinetic energy dissipates into the floor. Inputting calculated theoretical Mgh yields an inflated ratio W/Q.
Q3. Variant 3: How do food nutritional kilojoules (kJ) convert to nutritional dietary calories (kcal)?
Answer Key: 1 dietary Calorie (kcal) = 1000 physical calories = 4.186 kJ. Therefore, 2000 kJ translates to ~478 kcal.
Frequently Asked Questions & Misconceptions
How was the calorie originally defined? What is the official SI unit today?
The heat required to raise 1 gram of air-free water from 14.5°C to 15.5°C at 1 atm. Modern SI universally standardizes on the Joule (J).
Is rubbing your hands together to warm them equivalent to Joule's experiment?
Identical principle! Muscles perform mechanical work against skin sliding friction (W = f*s), converting 100% to internal thermal energy.
What did Count Rumford observe boring cannon barrels that undermined the caloric theory?
Dull drills continuously boiled water indefinitely without depleting cannon metal, proving heat cannot be a finite material substance.
Could you boil a cup of cold water purely by vigorously blending it inside a thermos?
Theoretically yes! Under perfect insulation, paddle blender mechanical work continuously pumps internal energy until 100°C boiling.