{title2=$Q$}
{wiki}

Heat is <energy> transferred across a <thermodynamic system>'s boundary because of a <temperature> difference. It is measured in <joules>, like <work> and <internal energy>. A hot cup transfers <heat> to cooler surroundings; its <temperature> describes its state, while the transferred <heat> describes a process. The cup stores <internal energy>, rather than a substance called <heat>. https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry[Ling, Moebs and Sanny, OpenStax, University Physics Volume 2, section 1.4: heat and internal energy]{ref}

For a <closed system> with unchanged bulk <kinetic energy> and <potential energy>, choose $Q>0$ for <heat> entering and $W>0$ for <work> done by the system. The <first law of thermodynamics> gives
$$
\Delta U=Q-W,\qquad dU=\delta Q-\delta W.
$$
Here $U$ is the stored <internal energy>. For example, a sealed piston cylinder receiving $20\,\mathrm{kJ}$ of <heat> and delivering $5\,\mathrm{kJ}$ of <work> gains $15\,\mathrm{kJ}$ of <internal energy>. A <closed system> retains its matter while exchanging <energy>; it need not be an <isolated system>. https://openstax.org/books/university-physics-volume-2/pages/3-3-first-law-of-thermodynamics[Ling, Moebs and Sanny, OpenStax, First law of thermodynamics and sign conventions]{ref}

\Image[/heat-work-internal-energy-balance.png]
{title=<Heat> input and <work> output determine the <internal energy> increase}
{description=The dashed boundary encloses a <closed system> in a sealed piston cylinder. The incoming arrow carries $Q=20\,\mathrm{kJ}$ of <heat>; the outgoing arrow carries $W=5\,\mathrm{kJ}$ of <work> done by the system. With unchanged bulk <kinetic energy> and <potential energy>, $\Delta U=15\,\mathrm{kJ}$. No matter crosses the boundary.}

Unlike <internal energy>, <heat> is not a <state function>: different paths between the same equilibrium states can transfer different $Q$, with compensating differences in <work>. The symbol $\delta Q$ records this dependence on the path; there is no stored quantity whose difference is always $Q$. The two paths in <first law of thermodynamics> illustrate this directly. Supplied <heat> can raise <temperature> as <sensible heat>, change a <phase fraction> through <latent heat>, or help supply expansion <work>. Measuring <temperature> alone therefore does not determine transferred <heat>.

For a <reversible thermodynamic process>, $\delta Q_{\rm rev}=T\,dS$, where $T$ is absolute <temperature> and $S$ is <entropy>. This identification requires reversibility: an irreversible <adiabatic process> has $Q=0$ and can nevertheless increase <entropy>. Likewise $Q=\Delta H$, with <enthalpy> $H$, requires the particular fixed-<pressure> conditions in <enthalpy>. These distinctions make <heat> useful as a precise boundary-transfer quantity in <heat engines>, <refrigerators> and heating calculations.

Historically, James Prescott Joule's paddle experiments showed that stirring <water> with input <work> could raise its <temperature>, helping establish <conservation of energy>. The lesson is still useful: a <temperature> rise can result from <work> even without incoming <heat>. https://openstax.org/books/university-physics-volume-2/pages/1-4-heat-transfer-specific-heat-and-calorimetry[Ling, Moebs and Sanny, OpenStax, section 1.4: Joule's paddle experiment]{ref}


 Heat (source code)