The average kinetic energy of the molecules of an ideal gas is directly proportional to what?

Answer 1

The energy is proportional to the absolute temperature.

The pressure expression is an immediate kinetic theory deduction.

#p = (mnv^2)/3#
Where #m# is mass of a gas molecule, #n# is no. of molecules per unit volume and #v# is the rms speed.
Thus, #n = N/V# where #N# is number of molecules.

Using this replacement,

#pV = (mNv^2)/3#
But, #(mv^2)/2 = E# is kinetic energy of a molecule.
Therefore, #pV = (2NE)/3#

In contrast, the ideal gas equation

#pV = muRT# where, #mu = N/N_A# is the number of moles.

With these findings,

#muRT = (2NE)/3#
#implies (NRT)/N_A = (2NE)/3#
Which finally gives, #E = (3kT)/2#
Where, #k = R/N_A# is the Boltzmann constant.

As a result, energy and temperature are proportionate.

This is how temperature is understood kinetically.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer 2

The average kinetic energy of the molecules of an ideal gas is directly proportional to the temperature of the gas.

Sign up to view the whole answer

By signing up, you agree to our Terms of Service and Privacy Policy

Sign up with email
Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7