Carnot Engine & Thermodynamic Cycle Physics

Efficiency: ---
Work: ---
QH: ---
QC: ---
600
300
15.0
5.0

What is the Carnot Engine Simulator?

Quick Answer: An interactive P-V diagram of an ideal Carnot heat engine. Adjust the hot and cold reservoir temperatures and volume limits to see the rectangular hyperbolic cycle (two isothermal and two adiabatic processes). Efficiency, net work, and heat transfers are computed live using thermodynamic formulas.

Theory of the Carnot Cycle

The Carnot cycle is the most efficient heat engine cycle operating between two temperatures. It consists of:
1. Isothermal expansion at TH (absorbing QH)
2. Adiabatic expansion (temperature drops to TC)
3. Isothermal compression at TC (rejecting QC)
4. Adiabatic compression back to TH.

Efficiency η = 1 - TC/TH. The work done is the area enclosed by the cycle on the P-V diagram. For an ideal gas, the adiabatic paths satisfy PVγ = constant, and isotherms are PV = nRT. The simulator uses γ = 1.4 and n=1 for simplicity.

Step-by-Step Examples

Example 1: High Efficiency Cycle

  1. Set TH = 800 K, TC = 300 K. Efficiency = 1 - 300/800 = 62.5%.
  2. Adjust max/min volume sliders to shape the cycle. The shaded work area represents net output.

Example 2: Low Temperature Difference

  1. Set TH = 400 K, TC = 350 K. Efficiency drops to 12.5%. The cycle becomes narrow.
  2. Observe how the adiabatic curves become nearly parallel to isotherms.

Example 3: Maximum Volume Influence

  1. Increase max volume to 25 L while keeping min volume at 5 L. The area expands, increasing net work even though efficiency remains the same.

Frequently Asked Questions

Why is the Carnot cycle rectangular on a P-V diagram?

The Carnot cycle is not rectangular; it is a curved shape bounded by two isothermal hyperbolas (PV=const) and two adiabatic curves (PVγ=const). It appears as a curved quadrilateral.

What does the shaded area represent?

The area enclosed by the cycle on the P-V diagram equals the net work done per cycle (in Joules).

How is efficiency calculated?

Carnot efficiency = 1 - TC/TH, where temperatures are in Kelvin. It depends only on reservoir temperatures.

Can I change the working gas?

The simulator assumes an ideal monatomic gas (γ=1.4). The cycle shape depends on γ; changing it would alter the adiabats.

Is this a realistic engine?

The Carnot cycle is an idealized reversible cycle. Real engines have irreversibilities and lower efficiencies.