Thermodynamics

First law of thermodynamics - formula in LaTeX

The energy balance of a system. Watch the sign convention: here W is the work done by the system. Some textbooks write the law with a plus sign, taking W as the work done on the system. The capital delta is \Delta.

\Delta U = Q - W

LaTeX code

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$$
\Delta U = Q - W
$$

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What the symbols mean

$\Delta U$: change in internal energy (J)
$Q$: heat supplied to the system (J)
$W$: work done by the system (J)

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

Worked example

A gas absorbs 500 J of heat and does 200 J of work as it expands. In this convention W is the work done BY the gas; textbooks using ΔU = Q + W give the same work a minus sign. \Delta is the capital delta, while the lowercase \delta marks an infinitesimal heat, δQ.

\Delta U = Q - W = 500\,\mathrm{J} - 200\,\mathrm{J} = 300\,\mathrm{J}

LaTeX commands in this formula

\Delta: capital Greek letter Delta

How to use this formula in LaTeX?

Copy the code with the button above - $$…$$ is centered display math.
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The formula works without extra packages.

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