rvanveshana.com
t = 0.00s
Pressure PVolume V
Stage: Isothermal Expansion (A โ†’ B)

Live Telemetry & Summary

Observe the indicator dot tracing out the PV work area (net work done is the enclosed loop area).

Hot Temp (T_H):500 K
Cold Temp (T_C):250 K
Max Efficiency (ฮท):50.0 %

Variable Adjuster

Hot Reservoir (T_H)500K
350600
Cold Reservoir (T_C)250K
150300

Carnot Engine Cycle

CARN

The Carnot Cycle is a theoretical ideal thermodynamic cycle that sets the maximum efficiency limit for heat engines operating between two temperatures. It consists of four reversible stages: isothermal expansion, adiabatic expansion, isothermal compression, and adiabatic compression.

ฮทmax=1โˆ’TCTH,Wnet=QHโˆ’QC\eta_{max} = 1 - \frac{T_C}{T_H}, \quad W_{net} = Q_H - Q_C

Whiteboard Solver Steps

Step 1

Carnot Heat Engine Efficiency Limit

The Carnot efficiency is the absolute thermodynamic limit for converting heat energy into work between two reservoirs.

ฮทmax=1โˆ’TCTH=1โˆ’250500=50.0%\eta_{max} = 1 - \frac{T_C}{T_H} = 1 - \frac{250}{500} = 50.0 \%
Step 2

Isothermal vs. Adiabatic Slopes

Adiabatic processes have steeper curves than isothermal ones because no heat is exchanged (Q=0), causing temperature to change dynamically.

(dPdV)adiabatic=โˆ’ฮณPV<โˆ’PV=(dPdV)isothermal\left(\frac{dP}{dV}\right)_{adiabatic} = -\gamma \frac{P}{V} < -\frac{P}{V} = \left(\frac{dP}{dV}\right)_{isothermal}