Fundamental Postulates of Thermal Physics and Heat Transfer

Fundamental Concepts and Assumptions

Temperature is a physical quantity whose value is an index of the degree of molecular kinetic energy.

Temperature Scales

Temperature scales are based on two fixed points:

• The conventional temperature scale.
• The absolute temperature scale (Kelvin, °K).

First Postulate: Temperature and Thermal Gradient

Temperature is a scalar quantity that, at each point, is a function of its position coordinates and time.

Defining the Thermal Gradient

If we consider a stationary field, we can define the gradient of $T$ at each point as a vector given by the expression:

This vector gives us the thermal gradient at each point of the field.

Statement of the First Postulate

The First Postulate states: "Heat is a form of energy exchange possible when there is a thermal gradient."

Heat is not a property inherent to substances, but rather a form of energy exchange between points where the temperature gradient is non-zero. We can say that heat is neither created nor destroyed, only transformed.

Second Postulate: Heat Capacity and Specific Heat

If a substance exchanges heat, temperatures vary. However, two different substances that receive the same amount of heat need not experience the same temperature change.

Key Definitions

• Heat Capacity (C): The amount of heat required to supply a substance to raise its temperature by one degree (depending on mass).
• Specific Heat (c): The heat required to supply one gram of that substance to raise its temperature by one degree.
• Calorie (Cal): The amount of heat required to supply one gram of water to raise its temperature by one degree Celsius in the range from 14.5 °C to 15.5 °C at 760 mm Hg pressure.

For solids in temperature ranges near room temperature, their specific heat can be considered constant.

Statement of the Second Postulate

The Second Postulate states: "In the temperature range, the specific heat remains constant."

Third Postulate: Heat Flow and Thermal Conductivity

When a thermal gradient exists (i.e., when the temperature gradient is not zero), energy is exchanged as heat.

Statement of the Third Postulate (Fourier's Law)

The Third Postulate states: "The amount of heat that passes through an area in unit time is proportional to the flow of the temperature gradient."

The coefficient of proportionality is called thermal conductivity. The temperature gradient vector points towards increasing values of temperature. Heat flows in the opposite direction (towards lower values of temperature).