The temperature of a sample of neon is raised from 20 degrees C to 40 degrees C, the average kinetic energy of the neon atoms changes by a factor of?
The answer is suppose to be 313/293, but I don't get how.
My idea was since average KE = (3/2) kT then the KE would only change by 2. Can you help explain this to me?
The average kinetic energy of atoms or molecules is proportional to the absolute temperature, T. You understand that already. (Note that is independent of atom or molecule weight!)
KE2/KE1 = (3/2)kT2/[(3/2)kT1] = T2/T1
The absolute temperature increases by a factor (273+40)/(273+20)= 313/293
So that is the answer.
Temperature should be in Kelvin
1/3
He is right
To understand why the average kinetic energy of the neon atoms changes by a factor of 313/293, we need to consider the relationship between temperature and kinetic energy.
The equation you mentioned, average KE = (3/2) kT, is known as the equipartition theorem. It relates the average kinetic energy of a molecule to its temperature. In this equation, k represents Boltzmann's constant.
However, in this case, we are not concerned with the ratio of the final average kinetic energy to the initial average kinetic energy. Instead, we need to find the factor by which the average kinetic energy changes when the temperature increases.
To determine how the average kinetic energy changes, we can compare the average kinetic energy at different temperatures using the equipartition theorem.
Let's denote the initial temperature as T1 and the final temperature as T2. We want to find the factor by which the average kinetic energy changes, denoted as x.
According to the equipartition theorem, the average kinetic energy is directly proportional to temperature: average KE = kT.
So, initially, the average kinetic energy is (3/2) kT1, and after the temperature increase, it becomes (3/2) kT2.
Now we can set up the equation:
(3/2) kT2 = x * (3/2) kT1
The k and (3/2) terms cancel out:
T2 = x * T1
To solve for x, we divide both sides of the equation by T1:
T2 / T1 = x
Now we substitute the given values:
T1 = 20 degrees C = 20 + 273.15 K (converting to Kelvin)
T2 = 40 degrees C = 40 + 273.15 K
Plugging in these values, we get:
(40 + 273.15) / (20 + 273.15) = x
Simplifying, we find:
313.15 / 293.15 = x
Therefore, the average kinetic energy changes by a factor of 313/293, which is approximately 1.068.