= Sensible heat
{title2=$Q_{\rm sens}$}
{wiki}
Sensible heat is transferred <heat> associated with a <temperature> change within a single <thermodynamic phase>. By contrast, <latent heat> can change the <phase fraction> while the <temperature> stays fixed during equilibrium <phase coexistence>. Neither name denotes an additional stored substance: both describe how transferred <heat> participates in a process.
For fixed <mass> $m$ and composition, use the <heat capacity> appropriate to the heating constraint. Under the <quasistatic process> assumptions in <heat capacity>, with only <pressure>-<volume (thermodynamics)> <work> and unchanged bulk <kinetic energy> and <potential energy>, fixed-<pressure> heating gives
$$
Q_{\rm sens}=m\int_{T_1}^{T_2}c_p(T)\,dT,
\qquad Q_{\rm sens}=mc_p(T_2-T_1)\quad\text{if }c_p\text{ is constant}.
$$
Here $c_p$ is <specific heat capacity at constant pressure>; fixed-<volume (thermodynamics)> heating instead uses <specific heat capacity at constant volume> $c_V$. A cooling step has negative $Q_{\rm sens}$ with the sign convention in <heat>. A <temperature> difference has the same numerical value in units of the <kelvin> or <degree Celsius>. The <integral> follows by adding the small transfers $\delta Q=mc_p(T)\,dT$, rather than assuming a constant <heat capacity>.
As a stylized <ice>-to-<water> example for a fixed-composition <closed system> at fixed <pressure> $1\,\mathrm{atm}$, take $m=0.5\,\mathrm{kg}$, an initial <temperature> of $-10\,{}^\circ\mathrm C$, <melting> at $0\,{}^\circ\mathrm C$, and a final <temperature> of $20\,{}^\circ\mathrm C$. Assume constant <specific heat capacity at constant pressure> values $c_{\rm ice}=2.1\,\mathrm{kJ\,kg^{-1}\,K^{-1}}$ and $c_{\rm water}=4.18\,\mathrm{kJ\,kg^{-1}\,K^{-1}}$, and <latent heat of fusion> $L_f=334\,\mathrm{kJ\,kg^{-1}}$. These are stipulated, rounded model values; ignore the container and <heat> losses, retain all the material, and assume only <pressure>-<volume (thermodynamics)> <work> under the <quasistatic process> conditions above. The three steps are
$$
\begin{aligned}
Q_{\rm ice}&=0.5\times2.1\times10=10.5\,\mathrm{kJ},\\
Q_{\rm melt}&=0.5\times334=167\,\mathrm{kJ},\\
Q_{\rm water}&=0.5\times4.18\times20=41.8\,\mathrm{kJ},\\
Q_{\rm total}&=10.5+167+41.8=219.3\,\mathrm{kJ}.
\end{aligned}
$$
Only the first and third terms are <sensible heat>; the middle term is <latent heat>. The plateau begins after $10.5\,\mathrm{kJ}$ and ends after $177.5\,\mathrm{kJ}$ of total supplied <heat>. At $94\,\mathrm{kJ}$ total input, half the <mass> is <liquid> <water> and the <temperature> remains $0\,{}^\circ\mathrm C$. The equilibrium <phase transition> <temperature> depends on <pressure>; this example stipulates a single fixed <pressure>. <University Physics Volume 2 by Samuel J. Ling and others/1.5 Phase Changes>{ref}
\Image[/sensible-and-latent-heating-curve.png]
{title=Heating $0.5\,\mathrm{kg}$ of <ice> to <water>: <sensible heat> and <latent heat>}
{description=Illustrative fixed-<pressure> <heating curve> using the constant parameters above. The sloping portions raise <temperature>; the long $0\,{}^\circ\mathrm C$ plateau changes the <phase fraction>. Total supplied <heat> is measured from the initial <ice> state and equals the <enthalpy> change under the stated assumptions.}
This split makes heating budgets easy to interpret: <melting> consumes $167/219.3\approx76.2\%$ of the supplied <heat> in this model despite causing no <temperature> rise. Within either single <thermodynamic phase>, the <heating curve> slope is $dT/dQ=1/(mc_p)$; a larger <heat capacity> makes the slope shallower. A flat interval represents changing <phase fraction>, so it cannot be modeled by applying $Q=mc_p\Delta T$ across the <phase transition>. The complementary constructed example in <latent heat> tracks that <phase fraction> explicitly.
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