Question
What is the formula for finding thermal energy
Answers
Answered by
GPT-4o
The formula for finding thermal energy (often referred to as heat, \( Q \)) depends on the context and the specific process involved. Here are a few commonly used formulas:
1. **For calculating thermal energy based on temperature change:**
\[
Q = mc\Delta T
\]
- \( Q \) is the thermal energy (in joules, J).
- \( m \) is the mass of the substance (in kilograms, kg).
- \( c \) is the specific heat capacity of the substance (in joules per kilogram per degree Celsius, J/(kg·°C) or J/(kg·K)).
- \( \Delta T \) (delta T) is the change in temperature (in degrees Celsius, °C, or Kelvin, K).
2. **For phase changes (e.g., melting, vaporization):**
\[
Q = mL
\]
- \( Q \) is the thermal energy (in joules, J).
- \( m \) is the mass of the substance (in kilograms, kg).
- \( L \) is the latent heat (latent heat of fusion for melting or latent heat of vaporization for boiling, in J/kg).
- The latent heat of fusion (\( L_f \)) is used for the phase change from solid to liquid or vice versa.
- The latent heat of vaporization (\( L_v \)) is used for the phase change from liquid to gas or vice versa.
3. **For thermal energy related to heat conduction (Fourier's Law of Heat Conduction):**
\[
Q = \frac{kA \Delta T t}{d}
\]
- \( Q \) is the heat transferred (in joules, J).
- \( k \) is the thermal conductivity of the material (in watts per meter per degree Celsius, W/(m·°C) or W/(m·K)).
- \( A \) is the area through which heat is being transferred (in square meters, m²).
- \( \Delta T \) is the temperature difference across the material (in degrees Celsius, °C, or Kelvin, K).
- \( t \) is the time duration over which heat transfer occurs (in seconds, s).
- \( d \) is the thickness of the material (in meters, m).
Each formula applies to different situations involving thermal energy, depending on whether you are dealing with temperature changes, phase changes, or heat transfer through a material.
1. **For calculating thermal energy based on temperature change:**
\[
Q = mc\Delta T
\]
- \( Q \) is the thermal energy (in joules, J).
- \( m \) is the mass of the substance (in kilograms, kg).
- \( c \) is the specific heat capacity of the substance (in joules per kilogram per degree Celsius, J/(kg·°C) or J/(kg·K)).
- \( \Delta T \) (delta T) is the change in temperature (in degrees Celsius, °C, or Kelvin, K).
2. **For phase changes (e.g., melting, vaporization):**
\[
Q = mL
\]
- \( Q \) is the thermal energy (in joules, J).
- \( m \) is the mass of the substance (in kilograms, kg).
- \( L \) is the latent heat (latent heat of fusion for melting or latent heat of vaporization for boiling, in J/kg).
- The latent heat of fusion (\( L_f \)) is used for the phase change from solid to liquid or vice versa.
- The latent heat of vaporization (\( L_v \)) is used for the phase change from liquid to gas or vice versa.
3. **For thermal energy related to heat conduction (Fourier's Law of Heat Conduction):**
\[
Q = \frac{kA \Delta T t}{d}
\]
- \( Q \) is the heat transferred (in joules, J).
- \( k \) is the thermal conductivity of the material (in watts per meter per degree Celsius, W/(m·°C) or W/(m·K)).
- \( A \) is the area through which heat is being transferred (in square meters, m²).
- \( \Delta T \) is the temperature difference across the material (in degrees Celsius, °C, or Kelvin, K).
- \( t \) is the time duration over which heat transfer occurs (in seconds, s).
- \( d \) is the thickness of the material (in meters, m).
Each formula applies to different situations involving thermal energy, depending on whether you are dealing with temperature changes, phase changes, or heat transfer through a material.