Understanding Energy Changes in Systems

Introduction

• Focus: Calculating energy stored or released as temperature changes.
• Key concept: Specific heat capacity.

Specific Heat Capacity

• Definition: Amount of energy required to raise the temperature of 1 kg of a substance by 1°C.
• Importance: Essential for calculating energy changes in substances.

Sample Problem 1: Water Heating

• Question: Calculate energy required to increase temperature of 2 kg of water from 20°C to 100°C.
• Specific Heat Capacity of Water: 4200 J/kg°C.
• Equation Used: [ \text{Change in thermal energy (J)} = \text{mass (kg)} \times \text{specific heat capacity (J/kg°C)} \times \text{temperature change (°C)} ]
• Values:
  • Mass: 2 kg
  • Temperature change: 80°C
• Calculation: [ \text{Change in energy} = 2 \times 4200 \times 80 = 67,200 \text{ J} ]
• Conversion to Kilojoules: 67,200 J / 1,000 = 67.2 kJ

Sample Problem 2: Aluminium Plate

• Question: Calculate thermal energy stored when temperature rises from 20°C to 200°C in a 1.5 kg aluminium plate.
• Specific Heat Capacity of Aluminium: 913 J/kg°C.
• Values:
  • Mass: 1.5 kg
  • Temperature change: 180°C
• Calculation: [ \text{Change in energy} = 1.5 \times 913 \times 180 = 246,510 \text{ J} ]
• Conversion to Kilojoules: 246,510 J / 1,000 = 246.51 kJ

Sample Problem 3: Hot Water Bottle

• Question: Calculate the mass of water in a water bottle that cools from 80°C to 20°C, releasing 76,000 J.
• Given:
  • Energy released: 76,000 J
  • Specific Heat Capacity of Water: 4200 J/kg°C
  • Temperature change: 60°C
• Rearranged Formula: [ \text{Mass (kg)} = \frac{\text{thermal energy change (J)}}{\text{specific heat capacity (J/kg°C)} \times \text{temperature change (°C)}} ]
• Calculation: [ \text{Mass} = \frac{76,000}{4200 \times 60} = 3 \text{ kg} ]

Conclusion

• By understanding and using the specific heat capacity, you can calculate energy changes in various systems.
• Practice with additional problems found in the revision workbook.