Matter Revision Notes

The Relationship Between Energy, Mass, Specific Heat Capacity and Temperature Change

The internal energy of a material changes when it is heated or cooled. This change in internal energy, specifically observed as a temperature change, can be quantified using the formula: Energy change (ΔE) = mass (m) × specific heat capacity (c) × temperature change (Δθ). This relationship is fundamental for understanding how different materials respond to energy transfer. The larger the mass, the more energy is required for a given temperature change. Similarly, a substance with a higher specific heat capacity needs more energy to achieve the same temperature increase compared to a substance with a lower specific heat capacity, assuming their masses are equal.

Understanding Specific Heat Capacity

Specific heat capacity (c) is a physical property of a substance that represents the amount of thermal energy required to raise the temperature of one kilogram (1 kg) of that substance by one degree Celsius (1 °C) or one Kelvin (1 K). Its units are Joules per kilogram per degree Celsius (J/kg°C) or Joules per kilogram per Kelvin (J/kgK). Materials with high specific heat capacities, like water, can store a lot of thermal energy without a large increase in their own temperature, which is why water is often used in central heating systems. Metals generally have lower specific heat capacities, meaning they heat up and cool down more quickly.

Units and Calculation Considerations

When applying the formula ΔE = mcΔθ, it is vital to ensure all units are consistent. Energy change (ΔE) is in Joules (J), mass (m) in kilograms (kg), specific heat capacity (c) in J/kg°C (or J/kgK), and temperature change (Δθ) in °C (or K). Both °C and K can be used for temperature change because a change of 1 °C is equivalent to a change of 1 K. Always convert units to the standard SI units if they are provided differently (e.g., grams to kilograms, kilojoules to joules) before calculation. Rearranging the formula allows calculation of any of the variables if the others are known, e.g., m = ΔE / (cΔθ) or Δθ = ΔE / (mc).

Understanding Specific Latent Heat

Specific latent heat (L) is the amount of energy absorbed or released per kilogram of a substance during a change of state, without a change in temperature. This energy is used to overcome or establish the intermolecular forces of attraction, rather than increasing the kinetic energy of the particles. There are two primary types: specific latent heat of fusion (Lᶠ) for solid-liquid transitions (melting/freezing) and specific latent heat of vaporisation (Lᶥ) for liquid-gas transitions (boiling/condensing).

The Energy Change Formula

The energy (E) involved in a change of state can be calculated using the formula: E = m × L. In this equation, 'E' represents the total energy in joules (J), 'm' is the mass of the substance in kilograms (kg), and 'L' is the specific latent heat in joules per kilogram (J/kg). It is essential to ensure that all units are consistent before performing any calculations. If mass is given in grams, convert it to kilograms first (1 kg = 1000 g).

Applying the Formula: Fusion and Vaporisation

When a substance melts, the energy required is calculated using E = m × Lᶠ. The same amount of energy is released when the substance freezes. When a substance boils or evaporates, the energy required is calculated using E = m × Lᶥ. The same amount of energy is released when the substance condenses. Always identify which phase transition is occurring to select the appropriate value of specific latent heat (Lᶠ or Lᶥ).

PAG 5: Investigating Specific Latent Heat

A practical investigation (PAG 5) involves determining the specific latent heat of fusion of ice. This typically involves measuring the mass of ice melted by an electrical heater, while also measuring the electrical energy supplied to the heater. The energy supplied by the heater can be calculated using E = P × t, where P is power and t is time. By equating this electrical energy to the energy required to melt the ice (E = m × Lᶠ), the specific latent heat of fusion can be determined. Control variables are important, such as ensuring the surrounding temperature does not contribute significantly to melting.