To determine the amount of thermal energy produced, we calculate the change in thermal energy using the formula that considers mass, specific heat capacity, and change in temperature.
Understanding Thermal Energy Production
Thermal energy, often referred to as heat, is associated with the movement of atoms and molecules within a substance. When this movement increases, the thermal energy also increases. This can happen when a substance is heated, or when other forms of energy are converted into thermal energy, like when friction converts kinetic energy into thermal energy.
Calculating Change in Thermal Energy
The specific formula to calculate the change in thermal energy is:
Change in Thermal Energy = mass × specific heat capacity × change in temperature
Here's what each component means:
- Mass (m): The amount of substance, typically measured in kilograms (kg).
- Specific Heat Capacity (c): The amount of energy required to raise the temperature of 1 kg of the substance by 1 degree Celsius (or 1 Kelvin). Measured in Joules per kilogram per degree Celsius (J/kg°C). Each substance has its own specific heat capacity.
- Change in Temperature (ΔT): The difference between the final temperature and the initial temperature. This is calculated as Final Temperature - Initial Temperature. Measured in degrees Celsius (°C) or Kelvin (K).
Steps to Calculate Thermal Energy Change
- Identify the Mass: Determine the mass of the substance that is undergoing a temperature change.
- Find the Specific Heat Capacity: Look up the specific heat capacity of the substance you're working with. Common materials have known specific heat capacities that are available in reference tables.
- Measure Initial and Final Temperatures: Record the initial temperature of the substance, and then measure the temperature again after the energy change has occurred.
- Calculate the Change in Temperature: Subtract the initial temperature from the final temperature. Make sure that the units are consistent (Celsius or Kelvin).
- Plug the Values into the Formula: Insert the mass, specific heat capacity, and change in temperature values into the formula: Change in Thermal Energy = m x c x ΔT.
- Calculate the Change in Thermal Energy: Do the calculation and the result is the change in thermal energy in Joules.
Example
Let's say we heat 2kg of water from 20°C to 40°C. Water's specific heat capacity is approximately 4186 J/kg°C.
- Mass (m): 2 kg
- Specific Heat Capacity (c): 4186 J/kg°C
- Initial Temperature: 20°C
- Final Temperature: 40°C
- Change in Temperature (ΔT): 40°C - 20°C = 20°C
- Plug Values into Formula: Change in Thermal Energy = 2 kg 4186 J/kg°C 20°C
- Calculate the Change in Thermal Energy: Change in Thermal Energy = 167440 Joules.
Therefore, approximately 167440 Joules of thermal energy were needed to heat 2kg of water from 20°C to 40°C.
Key Points
- The formula provides the change in thermal energy, not the total thermal energy in a system.
- Consistent units are crucial in the calculations.
- Specific heat capacity is a material-dependent constant and is usually readily available.
By following these steps and using the formula, you can effectively find how much thermal energy is produced or absorbed in various situations.
