Entropy & Heat Engines – AP Physics 2

2nd Law of Thermodynamics

$$ \Delta S_{univ} \ge 0 $$

The total entropy of the universe can never decrease. For any heat engine, total entropy generated must be zero (reversible) or positive (irreversible).

Entropy Change

$$ \Delta S = \frac{Q}{T} $$

Hot Res: Loses heat ($Q_H < 0$). $\Delta S_{Hot} < 0$.

Cold Res: Gains heat ($Q_C > 0$). $\Delta S_{Cold} > 0$.

Engine: Operates in a cycle. $\Delta S_{Eng} = 0$.

Tags

entropyheat engine2nd Lawcarnot

Hot Reservoir

1000 K

⇣

Heat Engine

Cycle $\Delta S = 0$

Work ($W$) ⇢

⇣

Cold Reservoir

300 K

Thermodynamic Ledger

Heat Extracted ($Q_H$):	1000 J
Work Done ($W$):
Heat Exhausted ($Q_C$):

Hot entropy change ($\Delta S_H$):
Cold entropy change ($\Delta S_C$):
Total Universe ($\Delta S_{univ}$):

Hot Reservoir $T_H$ (K) 1000 K

Cold Reservoir $T_C$ (K) 300 K

Target Efficiency ...

Ideal Carnot Efficiency: $\mathbf{e = 1 - T_C/T_H}$. An engine operating at this limit creates absolutely exactly zero net entropy.