Thermodynamics & Energy · AP Physics 2 Unit 2 (Thermodynamics)
Ideal Gas Law & p-V Thermodynamic Cycle Simulator
Key exam takeaway: In a p-V indicator diagram, the area enclosed by a cyclic loop represents net mechanical work performed. Clockwise cycles act as heat engines; counter-clockwise cycles act as refrigerators.
- Client-side
- No Sign-up
- Live Derivation
- Projector Mode
- Print Worksheet
3D Simulation Stage● 60 FPS
Parameter Controls
kPa
L
K
Live Derivations & Metrics
Gas Constant Product nR
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Boundary Work Done W
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Internal Energy Change ΔU
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Heat Exchanged Q
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Real-Time Formula Derivation
Governing Formula:
--Substitution:
--Regime: --
Worked Examples & Exam Question Deep Dive
Worked Problem
Problem: Gas at p1=100kPa, V1=2.0L, T1=300K is compressed isothermally to 1.0L. Find final pressure.
Step-by-Step Derivation:
- Isothermal Boyle's Law: p1*V1 = p2*V2 => p2 = (100kPa * 2.0L) / 1.0L = 200 kPa.
Worked Problem
Problem: Car tire is 200kPa at -3°C (270K). Summer heat raises air inside to 54°C (327K) at constant volume. Find new pressure.
Step-by-Step Derivation:
- Charles's Law: p2 = p1 * (T2/T1) = 200kPa * (327/270) ≈ 242 kPa.
Student Inquiry Worksheet & Practice Problems
Q1. Variant 1: Why must thermodynamic calculations use Kelvin rather than Celsius?
Answer Key: Must use absolute Kelvin (K = °C + 273.15)! State laws establish proportionalities anchored at absolute zero (0K); Celsius offsets break linearity.
Q2. Variant 2: State the First Law of Thermodynamics ΔU = W + Q and clarify sign conventions.
Answer Key: W > 0: work done ON system; W < 0: work done BY system. Q > 0: heat absorbed; Q < 0: heat rejected. ΔU > 0: internal energy increases.
Q3. Variant 3: In adiabatic expansion (Q = 0), does gas temperature rise or drop? Explain.
Answer Key: Temperature drops! By ΔU = W + Q with Q=0, expansion work by gas (W < 0) reduces internal energy ΔU < 0, cooling the gas.
Frequently Asked Questions & Misconceptions
Under what conditions do real gases behave like ideal gases?
At high temperatures and low pressures! Molecular volumes become negligible relative to total container volume, and intermolecular forces vanish.
When pumping a bicycle tire, why does the lower pump cylinder get hot?
Primarily adiabatic compression work! Forcefully compressing air does mechanical work on it, spiking gas temperature. Friction is negligible in comparison.
Why does a misty cloud form at the bottle neck when popping a champagne cork?
Rapid adiabatic expansion work drops gas temperature by dozens of degrees within milliseconds, instantly condensing surrounding water vapor into mist.
What is Absolute Zero (0K = -273.15°C)? Can experimentalists reach it?
Theoretical ground state where thermal kinetic motion drops to quantum zero-point energy. The Third Law of Thermodynamics proves it can never be reached.