Table of contents | |
Introduction | |
Thermal Equilibrium: Temperature | |
What Occurs at Thermal Equilibrium? | |
Thermal Equilibrium Formula |
An example of a water molecule engaging in random motion due to kinetic energy.
Now, let's consider the transfer of kinetic energy between two molecules in separate objects, rather than within the same object. The object with a lower temperature will have molecules possessing lower kinetic energy, whereas the object at a higher temperature will exhibit molecules with higher kinetic energy. When these objects are in thermal contact and their molecules can interact, the molecules with lower kinetic energy will gradually absorb more and more energy, subsequently transferring it to the molecules in the object with the lower temperature. This process continues over time until the average kinetic energy of the molecules in both objects becomes equal, resulting in both objects attaining an equal temperature. This state is known as thermal equilibrium, where the objects have achieved a balanced distribution of thermal energy.
When it comes to the transfer of heat energy, it's important to not fall into the trap of using temperature when the calculation is involved. Instead, the word energy is more appropriate, and therefore joules is the better unit. To determine the temperature of equilibrium between two objects of varying temperatures (hot and cold), we must first note that this equation is correct:
qhot + qcold = 0
This equation tells us that the heat energy qhot lost by the hotter object is the same magnitude but an opposite sign of the heat energy gained by the colder object qcold, measured in joules. Therefore, adding these two together is equal to 0.
Now, we can calculate the heat energy for both of these in terms of the object properties. To do so, we need this equation:
q = m.c . ΔT
Where m is the mass of the object or substance, measured in kilograms kg, ΔT, is the temperature change, measured in degrees Celcius ºc (or Kelvin ºk , as their magnitudes are equal) and is the specific heat capacity of the object, measured in joules per kilogram Celcius
The only thing we have left to determine here is the temperature change ΔT . As we're looking for the temperature at thermal equilibrium, the temperature change can be thought of as the difference between the equilibrium temperature Te and the current temperatures of each object Thc and Tcc. With the current temperatures being known, and the equilibrium temperature being the variable that we are solving for, we can assemble this rather large equation:
Where anything underscored with an h regards the hotter object, and anything underscored with a c regards the colder object. You may notice that we have the variable Te marked twice in the equation. Once all the other variables are put into the formula, you will be able to combine these into one, to find the final temperature of thermal equilibrium, measured in Celsius.
Example
A block of metal with a mass of 2 kg and a specific heat capacity of 0.5 J/g°C initially has a temperature of 100°C. It is placed in contact with a block of wood with a mass of 1 kg and a specific heat capacity of 1 J/g°C, which initially has a temperature of 20°C. Assuming no heat loss to the surroundings, what will be the equilibrium temperature when thermal equilibrium is reached?
To find the equilibrium temperature, we can use the formula:
(mass1 × specific heat capacity1 × temperature change1) + (mass2 × specific heat capacity2 × temperature change2) = 0
Let's plug in the given values and solve for the equilibrium temperature (Te):
(2 kg × 0.5 J/g°C × (Te - 100°C)) + (1 kg × 1 J/g°C × (Te - 20°C)) = 0
Now, let's simplify the equation:
(1 J/°C × (Te - 100°C)) + (1 J/°C × (Te - 20°C)) = 0
Simplifying further:
Te - 100°C + Te - 20°C = 0
2Te - 120°C = 0
2Te = 120°C
Te = 60°C
Therefore, when thermal equilibrium is reached, the equilibrium temperature will be 60°C.
In this example, the metal block and the wood block initially have different temperatures, and through the process of thermal contact and energy transfer, they reach a state of thermal equilibrium where their temperatures equalize.
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