Temperature Scales

Temperature measures the average kinetic energy of the particles in a substance. Three scales are in common use:

• Celsius (°C): Water freezes at 0 °C and boils at 100 °C at standard atmospheric pressure. Used worldwide in everyday life and in most laboratory science.
• Fahrenheit (°F): Water freezes at 32 °F and boils at 212 °F. Predominantly used in the United States.
• Kelvin (K): The SI base unit of thermodynamic temperature. Starts at absolute zero — the point at which particles have minimum thermal energy and particle motion effectively ceases.

The conversion between Celsius and Kelvin is:

$$T_K = T_C + 273.15$$

Example: Normal human body temperature is 37 °C.<br>$$T_K = 37 + 273.15 = 310.15\ \text{K}$$

A change of 1 °C equals a change of 1 K — the two scales share the same step size, differing only in their zero point.

Modes of Heat Transfer

Heat is thermal energy in transit — it flows spontaneously from a region of higher temperature to a region of lower temperature. There are three mechanisms by which this transfer occurs:

1. Conduction

Heat flows through a material by direct contact between neighbouring particles. Faster-moving (hotter) particles collide with slower (cooler) neighbours and pass energy along. Conduction is most efficient in solids, especially metals, where free electrons carry energy rapidly through the lattice. Example: a metal spoon left in a bowl of hot soup quickly becomes warm along its full length.

2. Convection

Heat is carried by the bulk movement of a fluid (liquid or gas). As fluid is heated it expands, becomes less dense, and rises; cooler, denser fluid sinks and takes its place, establishing a circular convection current. Example: a radiator warms the air immediately around it; that air rises and is replaced by cooler air from below, gradually heating the entire room.

3. Radiation

Heat is transferred as electromagnetic waves (primarily infrared), which can travel through a vacuum — no medium is required. All objects emit thermal radiation; hotter objects emit more intensely and at shorter wavelengths. Example: the Sun's energy travels 150 million km through the vacuum of space to reach Earth's surface.

Specific Heat Capacity

Different materials require different amounts of energy to raise their temperature by the same amount. Specific heat capacity ($c$) is defined as the heat energy required to raise the temperature of 1 kg of a substance by 1 K (equivalently, 1 °C). The governing equation is:

$$Q = mc\Delta T$$

where:

• $Q$ = heat energy transferred (joules, J)
• $m$ = mass of the substance (kg)
• $c$ = specific heat capacity ($\text{J kg}^{-1}\text{K}^{-1}$)
• $\Delta T$ = change in temperature (K or °C)

Worked example: How much heat energy is needed to raise 2.0 kg of water from 20 °C to 70 °C? The specific heat capacity of water is $c = 4200\ \text{J kg}^{-1}\text{K}^{-1}$.

$$\Delta T = 70 - 20 = 50\ \text{°C}$$<br>$$Q = mc\Delta T = 2.0 \times 4200 \times 50 = 420{,}000\ \text{J} = 420\ \text{kJ}$$

Water's exceptionally high specific heat capacity means it absorbs large amounts of energy with relatively small temperature rises — which is why it is used as a coolant in engines and is central to regulating Earth's climate.