# How to Calculate Thermal Energy in Temperature & Phase Changes

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Thermal energy is a measure of the activity of particles in a specimen. As a specimen absorbs heat, the particles become energetic. If enough energy is absorbed, the bonds between the particles may be broken, and the material changes phase. Boiling a kettle of water to make steam is a typical example of this process. The capacity to absorb energy is unique for each material and is described by a constant called the specific heat capacity. The amount of energy required for a phase change is also characteristic of the material, and is referred to as the latent heat.

### Things You'll Need

• Scale
• Specific heat capacity tables
• Latent heat tables
• Calculator

## Thermal Energy and Temperature Change

• Calculate the temperature difference. Subtract the final temperature from the initial temperature to find the temperature difference (T). For example, if the temperature changes from 60 degrees Celsius to 10 degrees Celsius during a cooling process, then the temperature difference is: T = -50 C = 10 C – 60 C = T(final) – T(initial).

• Look up the specific heat capacity (c) of the material undergoing the heating or cooling process. Each material has a unique specific heat capacity. These values are typically tabulated in materials or chemical handbooks. For example, the specific heat capacity of liquid water is 4186 J/(kgC).

• Measure the mass (m) of the specimen undergoing the heating or cooling process. Use a scale to measure the mass before or after the process.

• Calculate the thermal energy gained or lost during the process of heating or cooling. The thermal energy (Q) is obtained using the formula: Q = (m) x (c) x (T). For example, if 1 kg of water is cooled from 60 degrees Celsius to 10 degrees Celsius, then the thermal energy lost by the water during the cooling process is Q = -209300 J = (1 kg) x (4186 J/(kgC)) x (-50 C) = (m) x (c) x (T). The negative sign for thermal energy indicates a lost of energy and is associated with cooling. A positive value for Q results during a gain of energy typical of a heating process.

## Thermal Energy and Phase Change

• Look up the latent heat (L) of the material undergoing the phase change. Each phase change for a specific material has a unique latent heat. The change from solid to liquid or liquid to solid is characterized by the latent heat of fusion (Lf). The latent heat of vaporization (Lv) is associated with the gas-liquid phase change. These latent heat values are typically tabulated in materials or chemical handbooks. For example, the latent heat of fusion associated with the change of phase of ice to liquid water is 3.34 x 10^5 J/kg, while the latent heat of vaporization associated with the phase change from steam to liquid water is 2.26 x 10^6 J/kg.

• Measure the mass (m) of the specimen undergoing the phase change. The process of phase change is restricted to the time period during which there is no temperature change in the specimen. Use a scale to measure the mass. Measuring the mass of a gas specimen is difficult, so it is best to take the mass measurement before vaporization or after condensation.

• Calculate the thermal energy gained or lost during the process of phase change. The thermal energy (Q) is obtained using the formula: Q = (m) x (L), where L may represent Lf or Lv. For example, if 1 kg of liquid water at 100 degrees Celsius is boiled to form steam at 100 degrees Celsius, the thermal energy gained by the steam is: Q = 2.26 x 10^6 J = (1 kg) x (2.26 x 10^6 J/kg) = (m) x (Lv). In similar manner, the energy gained by 1 kg ice at 0 C converting to 1 kg of liquid water at 0 C is: Q = 3.34 x 10^5 J = (1 kg) x (3.34 x 10^5 J/kg) = (m) x (Lf).

## References

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