Understanding Internal Energy and Specific Heat Capacity

Key Concepts

Internal Energy: Total energy stored in the particles of a substance or system, consisting of potential and kinetic energy.
- Potential Energy: Includes gravitational and elastic potential, not directly related to temperature.
- Kinetic Energy: Movement energy of particles, directly affects temperature.
Temperature: Measure of the average internal energy of a substance.
- Higher internal energy results in a higher temperature.

Definition: Amount of energy needed to raise the temperature of 1 kg of a substance by 1°C.
Comparison:
- Water: 4200 J to raise 1 kg by 1°C.
- Mercury: 139 J to raise 1 kg by 1°C.
Cooling: Energy released when a substance cools by 1°C is equal to its specific heat capacity.

Change in Internal Energy: ( \Delta E = m \cdot c \cdot \Delta \theta )
- ( \Delta E ): Change in internal energy
- ( m ): Mass of the substance
- ( c ): Specific heat capacity
- ( \Delta \theta ): Change in temperature

Problem: Find the final temperature of 800g of water initially at 20°C after 20 kJ of energy is added.
- Specific heat capacity of water: 4200 J/kg°C
Solution:
1. Convert units:
  - 800g = 0.8 kg
  - 20 kJ = 20,000 J
2. Use formula to find temperature change:
  - ( \Delta \theta = \frac{E}{m \cdot c} )
  - ( \Delta \theta = \frac{20,000}{0.8 \cdot 4200} \approx 5.95°C )
3. Final temperature:
  - Initial temperature + temperature change: 20°C + 5.95°C = 25.95°C
  - Rounded to three significant figures: 26.0°C
Note: Real-life conditions may result in lower temperature increases due to heat loss to surroundings. Use insulation and lids in experiments.

Understanding internal energy and specific heat capacity is crucial in predicting temperature changes in substances when energy is added or removed.
Practical experiments should consider energy loss for accurate results.

Tip: Always round your final answer to the appropriate number of significant figures.