Sensible heat is the heat that causes a change in temperature of a substance without causing a change in its phase (state). When heat is added to or removed from a substance, the sensible heat is the energy that is responsible for the rise or fall in temperature.
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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 and composition, use the heat capacity appropriate to the heating constraint. Under the quasistatic process assumptions in heat capacity, with only pressure-volume work and unchanged bulk kinetic energy and potential energy, fixed-pressure heating givesHere is specific heat capacity at constant pressure; fixed-volume heating instead uses specific heat capacity at constant volume . A cooling step has negative 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 , rather than assuming a constant heat capacity.
As a stylized ice-to-water example for a fixed-composition closed system at fixed pressure , take , an initial temperature of , melting at , and a final temperature of . Assume constant specific heat capacity at constant pressure values and , and latent heat of fusion . These are stipulated, rounded model values; ignore the container and heat losses, retain all the material, and assume only pressure-volume work under the quasistatic process conditions above. The three steps areOnly the first and third terms are sensible heat; the middle term is latent heat. The plateau begins after and ends after of total supplied heat. At total input, half the mass is liquid water and the temperature remains . The equilibrium phase transition temperature depends on pressure; this example stipulates a single fixed pressure. [ref]
This split makes heating budgets easy to interpret: melting consumes of the supplied heat in this model despite causing no temperature rise. Within either single thermodynamic phase, the heating curve slope is ; a larger heat capacity makes the slope shallower. A flat interval represents changing phase fraction, so it cannot be modeled by applying across the phase transition. The complementary constructed example in latent heat tracks that phase fraction explicitly.