5. Specific Heat Capacity | Internal Energy & Temperature

1. Internal Energy and Particle Motion

Defining Internal Energy

  • Internal Energy: The total energy stored by the particles that make up a substance or system.

  • Two Components: It is the sum of the potential energy stores (chemical bonds, etc.) and the kinetic energy stores (movement of particles).

  • Connection to Temperature: Temperature is specifically a measure of the average kinetic energy of the particles in a substance.

Heating and Energy Transfer

  • When a substance is heated, energy is transferred to the kinetic energy stores of the particles.

  • This increase in kinetic energy causes the particles to move faster, which results in a rise in temperature.

2. Specific Heat Capacity (SHC)

Definition

  • Specific Heat Capacity: The amount of energy required to raise the temperature of 1 kilogram of a substance by 1 degree Celsius.

  • Cooling: SHC also represents the energy released when a substance cools. For example, if water cools by 1°C, it releases the same amount of energy it needed to heat up by 1°C.

Comparative Examples

  • Water: Has a high SHC (4,200 J/kg°C). It requires a lot of energy to heat up and holds onto heat well.

  • Mercury: Has a low SHC (139 J/kg°C). It heats up and cools down much more quickly with less energy.

3. The Specific Heat Capacity Equation

The Formula

ΔE = m × c × Δθ

  • ΔE (Change in Thermal Energy): Measured in Joules (J).

  • m (Mass): Measured in kilograms (kg).

  • c (Specific Heat Capacity): Measured in J/kg°C.

  • Δθ (Change in Temperature): Measured in degrees Celsius (°C). The symbol θ (theta) represents temperature.

Rearranging the Formula

To find the temperature change (Δθ), the formula is rearranged to:

Δθ = ΔE / (m × c)

4. Practical Application and Accuracy

Calculation Tips

  • Unit Conversions: Always convert grams to kilograms (divide by 1,000) and kilojoules to Joules (multiply by 1,000).

  • Significant Figures: Final answers should generally be rounded to three significant figures for exam accuracy.

Experimental Realities

  • Energy Loss: In a real-world experiment, the temperature rise is often lower than calculated because heat energy escapes to the surroundings.

  • Prevention: To improve accuracy in a lab, use insulation and a lid to minimize energy loss.

5. Summary Table of Units

Variable

Symbol

Standard Unit

Change in Energy

ΔE

Joules (J)

Mass

m

Kilograms (kg)

Specific Heat Capacity

c

J/kg°C

Temperature Change

Δθ

Degrees Celsius (°C)