% miko:type: atomic
% miko:title: First Law of Thermodynamics
% miko:summary: Energy conservation written for heat, work, and internal energy.
% miko:tags: thermo
% miko:difficulty: intro
% miko:related: entropy-second-law, heat-capacity, thermodynamic-potentials
% miko:keywords: internal energy, heat, work

\documentclass{article}
\usepackage{amsmath}
\title{First Law of Thermodynamics}
\begin{document}
\maketitle

\section{Statement}

For a closed system,

$$
dU=\delta Q-\delta W.
$$

Here $U$ is internal energy, $\delta Q$ is heat added to the system, and
$\delta W$ is work done by the system. For simple compressible matter,

$$
\delta W=p\,dV,
$$

so a reversible quasistatic process satisfies

$$
dU=T\,dS-p\,dV.
$$

\section{Meaning}

The first law does not say which processes occur spontaneously. It only
conserves energy. Directionality enters through entropy and the second law.

\end{document}
