Thermodynamics

Carnot efficiency - formula in LaTeX

The highest efficiency any heat engine can reach between two temperatures. Both temperatures must be in kelvins, otherwise the result is meaningless. The Greek letter eta is \eta.

$$
\eta = 1 - \dfrac{T_2}{T_1}
$$

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What the symbols mean

$\eta$

efficiency (a number from 0 to 1)

$T_1$

temperature of the hot reservoir (K)

$T_2$

temperature of the cold reservoir (K)

A thermodynamics formula - useful for gas processes, heat balances and physical chemistry.

Worked example

An engine running between a 500 K source and 300 K surroundings can turn at most 40% of the heat into work. Write the percent sign with a backslash, \%: a bare % starts a comment in LaTeX and cuts off the rest of the line.

LaTeX commands in this formula

\eta

Greek letter eta

\dfrac

fraction (display)

x_{0}

subscript; wrap several characters in braces

How to use this formula in LaTeX?

1. Copy the code with the button above - $$…$$ is centered display math.
2. Paste it into the CamteX editor, Overleaf or any LaTeX document.
3. Inside a sentence, use single $…$ instead of double.
4. The formula needs the amsmath package - CamteX templates include it in the preamble.

Related formulas - Thermodynamics

• Ideal gas law
• First law of thermodynamics
• Heat
• Gibbs free energy