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Welcome to our Physics lesson on Translational Kinetic Energy of Gas, this is the second lesson of our suite of physics lessons covering the topic of Pressure, Temperature and RMS Speed, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Let's consider again the molecule in the cubic container of the previous paragraph. The kinetic energy of this molecule is
We substitute in this equation the value of rms speed found earlier:
or
Given that NA = M/m, where m is the mass of a single molecule, we obtain:
Having k = R/NA, where k is the Boltzmann constant, we obtain
Therefore, we obtain a very important conclusion based on the last formula:
"All ideal gas molecules, no matter what kind of gas they belong, have the same translational kinetic energy at a given temperature."
This means that when we measure the temperature of an ideal gas, we are actually measuring the average translational kinetic energy of its particles. We have sustained earlier this theory of correspondence between average kinetic energy of particles and temperature when explaining the meaning of temperature but now, we are also proving it mathematically.
What is the translational kinetic energy of 0.02 moles of an ideal gas at 227°C?
The formula
gives the translational kinetic energy of a single molecule of an ideal gas, not of the entire gas.
Given this, we must multiply the kinetic energy of a single particle to the number of particles in 0.02 moles of ideal gas, considering also the fact that 227°C correspond to 500 K (227 + 273 = 500). Thus, we have:
You have reached the end of Physics lesson 13.7.2 Translational Kinetic Energy of Gas. There are 3 lessons in this physics tutorial covering Pressure, Temperature and RMS Speed, you can access all the lessons from this tutorial below.
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