# Energy and Temperature

This topic is part of the HSC Physics course under the section Thermodynamics.

### HSC Physics Syllabus

• explain the relationship between the temperature of an object and the kinetic energy of the particles within it (ACSPH018)
• analyse the relationship between the change in temperature of an object and its specific heat capacity through the equation 𝑄=𝑚𝑐Δ𝑇 (ACSPH020)

### Temperature and Kinetic Energy Temperature is a measure of the average translational kinetic energy of the particles in a substance. Whether they're atoms, molecules, or ions, all particles in matter are constantly in motion—vibrating, rotating, or moving about. The temperature reflects the energy associated with this motion.

The Celsius and Kelvin scales are both units of temperature measurement, but they have distinct origins, reference points, and uses. Here's a comparison:

### Units of Temperature Celsius (C)

The unit of Celsius is defined by the freezing and boiling points of water:

• Freezing Point: Defined as 0°C, it's the temperature at which water freezes under normal atmospheric pressure.
• Boiling Point: Defined as 100°C, it's the temperature at which water boils under normal atmospheric pressure.

Kelvin (K)

The unit of Kelvin is defined by:

• Absolute Zero: Defined as 0 K, it's the theoretical temperature at which particles have the minimum possible kinetic energy and essentially cease their motion. It's equivalent to -273.15°C.
• Triple Point of Water: Defined as exactly 273.16 K, it's the unique temperature at which water can coexist in solid, liquid, and gaseous forms simultaneously. This provides a more fundamental thermodynamic reference point than the boiling or freezing of water.

Key points:

• The Kelvin scale is the standard unit of temperature in the physical sciences like physics and chemistry.
• It's especially significant in studies related to absolute temperature, like in thermodynamics and low-temperature physics.
• Kelvin temperatures are always positive since they start from absolute zero.

Celsius vs Kelvin

The Celsius and Kelvin scales are offset by 273.15. To convert from Celsius to Kelvin, you add 273.15, and to convert from Kelvin to Celsius, you subtract 273.15.

### What is Heat?

Heat refers to the transfer of energy between objects or systems due to a temperature difference. Heat always flows from an object with a higher temperature to one with a lower temperature until thermal equilibrium is reached.

Heat transfer causes changes in temperature and phase in substances. For instance, when heat is added to ice, its temperature rises, and it can melt into water.

The amount of heat required to change the temperature of a substance depends on the substance's specific heat capacity (discussed below), its mass, and the desired temperature change.

Kinetic energy is always present in particles with temperature above absolute zero, even if there's no heat transfer. Heat, on the other hand, exists only when there's a temperature difference and ceases once thermal equilibrium is achieved.

### Energy, Temperature Change, and Specific Heat Capacity

The amount of heat energy required to change the temperature of an object depends on three factors:

1. The mass of the object (m).
2. The material the object is made from, quantified by its specific heat capacity (c).
3. The desired change in temperature (\Delta T).

The relationship can be described by the equation:

$$Q = mc\Delta T$$

Where:

• Q is the heat energy absorbed or released.
• m is the mass of the object.
• c is the specific heat capacity of the material (energy required to raise the temperature of 1 kg of the material by 1°C or K).
• \DeltaT is the change in temperature in °C or K).

It is important to note that \Delta T can be expressed in either degree Celsius or Kelvin without adding or subtracting 273.15.

For example when temperature of water increases from 25ºC to 100ºC, the temperature change is 75ºC. In terms of Kelvins, the temperature of water increases from 298.15 K to 373.15 K, which is a temperature change of 75 K.

### What is Specific Heat Capacity?

This is defined as the amount of heat required to change the temperature of a particular quantity of a substance. Substances with higher specific heat capacity values require more heat to change in temperature.

For example, the specific heat capacity of water is 4184 J kg–1 K–1. This means exactly 4184 J of heat is required to raise the temperature of 1 kg of water by 1 Kelvin or Celsius. This is a relatively high value.

The specific heat capacity of aluminium metal is 890 J kg–1 K–1. This means exactly 890 J of heat is required to raise the temperature of 1 kg of aluminium by 1 Kelvin or Celsius. This lower specific heat capacity value compared to water means less energy is required to change the temperature of 1 kg of aluminium than 1 kg of water.

### Example 1

Calculate the change in temperature of 300.0 g of water when 20 000 J of heat energy is transferred to the water sample. Specific heat capacity of water = 4184 J kg–1 K–1