PHYSICS VIRTUAL LAB — THERMODYNAMICS

Carnot Principle

Reversible Heat Engine & Carnot Cycle Simulator

CYCLE READY

Experiment Parameters & Cycle Controls

Interactive Simulator
Hot Reservoir (TH) 600 K
Cold Reservoir (TC) 300 K
Initial Volume (V1) 1.00 L
Initial Pressure (P1) 4.00 atm
Cycle Speed 1.0x
Current Cycle Stage
STAGE 1 1 — ISOTHERMAL EXPANSION
Working fluid remains at T = TH. Gas absorbs heat QH from hot reservoir, expands, and pushes the piston outward.
STAGE PROGRESS
0%
1
Isothermal Expansion
T = TH | Absorbs QH
2
Adiabatic Expansion
Q = 0 | TH → TC
3
Isothermal Compression
T = TC | Rejects QC
4
Adiabatic Compression
Q = 0 | TC → TH

Reversible Carnot Heat Engine & Piston Assembly

SVG Live Apparatus
HOT RESERVOIR TH = 600 K COLD RESERVOIR TC = 300 K THERMAL CONTACT (TH) T = 600 K P=4.00 atm | V=1.00 L WORK OUTPUT (W) W = 277.2 J QH = 554.5J QC = 277.2J

P-V Diagram (Pressure vs Volume)

Real-time Plot
Enclosed Area = Net Work (Wnet = ∮P dV) V: 1.00L | P: 4.00atm

T-S Diagram (Temperature vs Entropy)

Isentropic Cycle
Rectangle Area = Heat QH / Work Wnet S: 0.92 J/K | T: 600K
Carnot Thermal Efficiency (ηCarnot)
50.0%
η = 1 − TC/TH = 1 − 300/600
Heat Input from Hot Res. (QH)
554.5 J
Absorbed at TH = 600 K
Heat Rejected to Cold Res. (QC)
277.2 J
Released at TC = 300 K
Net Work Produced (Wnet)
277.3 J
W = QH − QC
Total Entropy Generation (ΔStotal)
0.000 J/K
Reversible Cycle: ΔShot + ΔScold = 0

Instantaneous Working Fluid State Monitor

Real-time Telemetry
Pressure (P)
4.00 atm
405.3 kPa
Volume (V)
1.00 L
0.00100 m³
Temperature (T)
600.0 K
326.9 °C
Stage Heat (Q)
+120.5 J
Heat Input
Stage Work (W)
+120.5 J
Expansion Work

Thermodynamic Observation Table — Carnot Cycle

4 Reversible Processes
Stage Thermodynamic Process Temperature (T) Pressure (P) Volume (V) Heat Transfer (Q) Work Done (W) Entropy Change (ΔS)
1 Isothermal Expansion TH = 600 K 4.00 → 2.22 atm 1.00 → 1.80 L QH = +554.5 J +554.5 J +0.924 J/K
2 Adiabatic Expansion 600 → 300 K 2.22 → 0.39 atm 1.80 → 5.09 L Q = 0 J +623.5 J 0.000 J/K
3 Isothermal Compression TC = 300 K 0.39 → 0.71 atm 5.09 → 2.83 L QC = -277.2 J -277.2 J -0.924 J/K
4 Adiabatic Compression 300 → 600 K 0.71 → 4.00 atm 2.83 → 1.00 L Q = 0 J -623.5 J 0.000 J/K

Comparison Panel — Reversible Carnot Engine vs Real-World Engines

Carnot's Theorem
Ideal Carnot Engine Reversible (ηmax)
  • Maximum Theoretical Efficiency: Achieves ηCarnot = 1 − TC/TH, which is strictly bounded by reservoir temperatures.
  • Zero Entropy Generation: Reversible processes ensure ΔStotal = 0 J/K (Sgen = 0).
  • Quasi-Static Execution: Infinite time is allowed for heat transfer across infinitely small temperature gradients (dT → 0).
  • Frictionless Operation: Zero mechanical friction between piston and cylinder walls, zero viscous fluid losses.
  • Perfect Insulation: Perfect adiabatic isolation during stages 2 and 4 (Q = 0).
Real Mechanical Engine Irreversible (η < ηmax)
  • Lower Efficiency Bounded by Carnot: Real efficiency is always strictly lower than Carnot efficiency (ηreal < ηCarnot).
  • Positive Entropy Generation: Irreversibilities generate entropy: ΔStotal > 0 (Sgen > 0).
  • Finite Rate Heat Transfer: Requires finite temperature differences (ΔT > 0) to transfer heat within practical cycle times.
  • Friction & Viscosity: Piston friction, gas turbulence, and pressure drop reduce usable mechanical work.
  • Thermal Stray Heat Losses: Unwanted conduction, convection, and radiation losses occur through engine walls.

Educational Thermodynamics Guide & Engineering Applications

Theory & Principles

What is the Carnot Principle?

Formulated by Nicolas Léonard Sadi Carnot in 1824, the Carnot Principle establishes the fundamental upper limit on the efficiency of any heat engine operating between two thermal reservoirs at temperatures TH and TC.

ηmax = 1 − (TC / TH)

Key takeaway: No heat engine can be more efficient than a Carnot engine operating between the same two temperature reservoirs!

The 4 Ideal Reversible Processes

  • Stage 1 — Isothermal Expansion: Gas absorbs heat QH at constant TH from hot reservoir while expanding.
  • Stage 2 — Adiabatic Expansion: Gas expands with Q = 0 until its temperature cools down to TC.
  • Stage 3 — Isothermal Compression: Gas rejects heat QC at constant TC to cold reservoir while being compressed.
  • Stage 4 — Adiabatic Compression: Gas is compressed with Q = 0 until its temperature rises back up to TH.

Entropy & Reversibility

A reversible process proceeds without any dissipation of energy into internal friction or turbulence. For a closed Carnot cycle:

oint (dQ / T) = (QH / TH) − (QC / TC) = 0

Because QH / TH = QC / TC, the net change in entropy for the universe per cycle is zero (ΔStotal = 0).

Engineering & Real-World Applications

  • Thermal Power Plant Analysis: Benchmarking Rankine and Combined Cycle power plants against ideal Carnot limits.
  • Internal Combustion Engines: Guiding efficiency optimizations in Otto and Diesel cycles.
  • Gas Turbines & Aviation: Estimating peak performance limits of Brayton cycle engines.
  • Refrigeration & Heat Pumps: Reverse Carnot cycle serves as the benchmark for COP in cooling and heating.