Heat

Energy transferred between systems due to a temperature difference. Theory, formulas, worked examples and interactive graphs.

Conceptual context

Heat is one of the most misunderstood concepts in physics. In everyday language people talk about "stored heat" in a body, about "having heat" or "losing heat", but these expressions are physically incorrect. In thermodynamics, heat is not a property of the system: it is energy in transit, a transfer process that occurs only when a temperature difference exists between two systems.

This leaf sits within the heat and thermal effects block, as a prerequisite for understanding calorimetry and the first law of thermodynamics. Understanding heat as a process rather than a substance is the conceptual prerequisite for all subsequent thermodynamics.

The concept of heat is intimately linked to that of temperature, but they are radically different quantities: temperature describes the state of a system, while heat describes an exchange between systems. Distinguishing these two concepts with precision is the first conceptual leap in thermodynamics.

🟢 Essential level

When you touch a hot object, you feel that "heat passes" into your hand. This accurately describes what happens: energy flows from the hotter body to the cooler one. That energy flow is what we call heat $Q$.

Heat does not exist as a property of a body; it only exists during the transfer process. Once the two bodies reach equilibrium, heat has ceased. What remains is a new equilibrium temperature, not "accumulated heat".

The amount of heat absorbed by a body depends on three factors: how much matter is present ($m$), what material it is made of ($c$), and how much its temperature changes ($\Delta T$). Different materials respond very differently to the same energy input: water needs far more heat than iron to warm by the same amount.

A useful essential-level distinction is to separate two questions: how much energy is transferred, and what observable effect it produces. If temperature does not change during a transition, energy is still entering or leaving, but it does not show up as warming.

🔵 Formal level

Basic formulas

Heat transfer without phase change — called sensible heat — follows the relation:

Sensible heat

Here $Q$ is the energy transferred in joules, $m$ the mass in kilograms, $c$ the specific heat capacity of the material in J/(kg·K), and $\Delta T$ the difference between final and initial temperature in kelvin or degrees Celsius.

The sign of $Q$ is crucial: if $\Delta T$ is positive (the system heats up), $Q$ is positive and the system absorbs heat. If $\Delta T$ is negative (the system cools down), $Q$ is negative and the system releases heat to the surroundings.

When the process involves a phase change — melting, vaporization, solidification, or condensation — temperature remains constant throughout the entire transition even though energy is being transferred. In that case, the exchanged heat is latent heat:

Latent heat

where $L$ is the specific latent heat of the material (in J/kg). The sign of the complete process depends on the direction of the transition: melting and vaporization are endothermic ($Q$ > 0), while solidification and condensation are exothermic ($Q$ < 0).

Real student questions

Why does water take so long to boil but cools quickly in a glass? Heating to 100 °C involves sensible heat with a high $c$, requiring large amounts of energy. Once the water is at room temperature in a glass, heat release to the surroundings is a continuous but slower process than the concentrated heat source of the stove. The asymmetry between heating (concentrated source) and cooling (dissipation at ambient temperature) explains the perceived difference in rates.

If temperature does not change during melting, does that mean no energy is being transferred? No. During melting exactly $Q$ = $m$ · $L$ of energy is transferred, but that energy is invested in breaking the crystalline structure of the solid, not in increasing thermal agitation. That is why temperature stays constant: average agitation does not increase, but intermolecular potential energy does.

Does the specific heat capacity of water change with temperature? Yes, though modestly in the usual range. Between 0 °C and 100 °C the $c$ of water varies by less than 1 %, so it can be treated as constant for standard calculations. At extreme temperatures or in other phases (ice or steam), specific heat changes significantly.

Why does heat depend on the path and not just on the initial and final states? Because heat is not a state function. The system can reach from A to B by many different thermodynamic paths (at constant pressure, at constant volume, combinations), and on each path the exchanged heat is different. Only internal energy and entropy are state functions; heat and work are path functions.

Final synthesis

Heat $Q$ is energy in transit driven by a temperature difference. Its magnitude in processes without phase change depends linearly on mass, material specific heat, and temperature change; during a phase change, it depends on mass and latent heat. The sign of $Q$ is the most relevant information about the process: it determines whether the system gains or loses energy and is in all cases consistent with the sign of $\Delta T$.