Average kinetic energy is proportional to absolute temperature
The average translational kinetic energy of the gas molecules is directly proportional to the absolute temperature of the gas.
What is Average kinetic energy is proportional to absolute temperature?
Temperature measured on a scale where absolute zero (0 Kelvin) is the lowest possible temperature, corresponding to the theoretical absence of all thermal energy.
Key formula / rule: Average Translational Kinetic Energy per Molecule
Key points
- Understand the relationship between average kinetic energy and absolute temperature.
- Quantify the average translational kinetic energy of gas molecules.
- Explain the significance of absolute zero in terms of molecular motion.
- Differentiate between translational, rotational, and vibrational kinetic energy.
Common exam trap
Confusing Celsius with Kelvin for temperature calculations.
Definitions
- Term
Absolute Temperature
- Meaning
Temperature measured on a scale where absolute zero (0 Kelvin) is the lowest possible temperature, corresponding to the theoretical absence of all thermal energy.
- Term
Translational Kinetic Energy
- Meaning
The kinetic energy associated with the linear motion of an object or molecule from one point to another.
- Term
Boltzmann Constant (k)
- Meaning
A physical constant that relates the average kinetic energy of particles in a gas with the absolute temperature of the gas. Its value is approximately $1.38 \× 10-23 J/K$.
Learning objectives
Understand the relationship between average kinetic energy and absolute temperature.
Quantify the average translational kinetic energy of gas molecules.
Explain the significance of absolute zero in terms of molecular motion.
Differentiate between translational, rotational, and vibrational kinetic energy.
Formulae
- Name
Average Translational Kinetic Energy per Molecule
- Note
k is the Boltzmann constant, T is the absolute temperature in Kelvin.
- Expression
Eavg = \frac{3}{2} kT
- Name
Total Kinetic Energy of N Molecules
- Note
N is the number of molecules.
- Expression
Etotal = N \× \frac{3}{2} kT
Prerequisites
Kinetic Theory of Gases
Ideal Gas Law
Temperature (Absolute Scale)
Kinetic Energy
Common mistakes
Confusing Celsius with Kelvin for temperature calculations.
Assuming kinetic energy is proportional to Celsius temperature.
Forgetting that the proportionality is for *translational* kinetic energy.
Applying the formula to non-ideal gases without considering deviations.
Keywords
Kinetic Theory of Gases
Average Kinetic Energy
Absolute Temperature
Boltzmann Constant
Ideal Gas
Molecular Motion
Practice preview
At absolute zero temperature (0 Kelvin), the average translational kinetic energy of an ideal gas molecule is:…
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If the average kinetic energy of gas molecules in a container is E, and the absolute temperature is T. If the temperature is increased to 2T, the new average kinetic energy will be:…
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Consider two ideal gases, Gas A and Gas B, at the same temperature. If Gas A has molecules with half the mass of Gas B, what is the ratio of their average translational kinetic energies?…
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