Heat guide
Heat vs Temperature
Temperature describes thermal state. Heat describes energy transferred because of a temperature difference. The two quantities are related, but they are not interchangeable.
Temperature is a state variable
Temperature is a property of a system that helps determine the direction of spontaneous heat transfer. Two objects at the same temperature can have very different masses, compositions and total internal energies.
Heat describes transfer
Heat appears when energy crosses a boundary because of a temperature difference. Saying that an object “contains heat” is convenient everyday language, but thermodynamics describes the stored quantity as internal energy.
Why a bathtub can contain more thermal energy than a cup of hot water
A cup can have a higher temperature while the bathtub contains much more mass. The energy associated with changing temperature depends on mass and specific heat capacity as well as temperature change.
Temperature scales
Celsius and Fahrenheit set convenient reference points, while kelvin is an absolute thermodynamic scale. Temperature differences expressed in kelvin and degrees Celsius have the same numerical size, but absolute-temperature equations such as thermal-radiation laws require kelvin.
What a thermometer measures
A thermometer reaches a thermal interaction with the object or environment being measured. Its reading becomes useful when the sensing element and target reach a sufficiently representative thermal state.
The same heat input can produce different temperature changes
Temperature response depends on how much material is present and how much energy that material requires per degree of temperature change. In the constant-property approximation, Q = mcΔT. A 10 kJ input therefore produces a much larger temperature rise in a small mass with low specific heat than in a large mass of water.
This is why temperature alone cannot tell you how much energy was transferred. You also need information about the material, mass, phase and process.
Thermal equilibrium gives temperature its practical role
When two systems can exchange energy thermally and no net heat transfer remains between them, they are in thermal equilibrium. Temperature is the property that becomes equal under that condition. This idea underlies practical thermometry: the sensor must interact with the target closely enough for its reading to represent the target condition.
Real measurements can still be distorted by poor contact, radiation from nearby surfaces, airflow, sensor response time or placing the sensor where the temperature is not representative.
Why two objects at the same temperature can contain different thermal energy
Temperature describes the thermal state of a system, while the energy associated with that state also depends on how much material is present and what the material is. A bathtub and a cup can both be at 40 °C, yet the bathtub generally contains far more internal energy because it contains much more water. This is why temperature alone cannot tell you how much energy must be removed to cool an object.
The same distinction appears when comparing materials. Equal masses of water and aluminium can start at the same temperature, but water requires much more energy for the same temperature change because its specific heat capacity is much larger.
Temperature difference drives heat transfer, not absolute temperature by itself
Heat transfer requires a driving difference between systems that can exchange energy. A 60 °C object in a 20 °C room tends to lose heat, while the same object in a 100 °C environment can gain heat. The object temperature has not changed, but the direction of heat transfer has reversed because the surroundings changed.
This is why thermal calculations almost always need both the object state and the boundary conditions around it.