Peoples Physics Concepts

http://www.ck12.org Chapter 18. Thermodynamics and Heat Engines

motionof the molecules. If the molecules had been able to rotate as well as move around the box, they could have

had the same kinetic energy with slower translational velocities, and, therefore, lower temperature. In other words,

in that case, or assumption that the kinetic energy of the atoms only depends on their velocities, implied between

equations [2] and [3],would not have held. Therefore,the number of degrees of freedom in a substance

determines the proportionality between molecular kinetic energy and temperature: the more degrees of

freedom, the more difficult it will be to raise its temperature with a given energy input. This is why it takes

so long to boil water but so little time to heat up a piece of metal with the same mass.

A note about the above discussion:

Since the objects at the basis of our understanding of thermodynamics are atoms and molecules, quantum effects can

make certain degrees of freedom inaccessible at specific temperature ranges. Unlike most cases in your current

physics class, where these can be ignored, in this case, quantum effects can make an appreciable difference.

For instance, the vibrational degrees of freedom of diatomic gas molecules discussed above are, for many gases,

inaccessible in very common conditions, although we do not have the means to explain this within our theory. In

fact, this was one of the first major failures of classical physics that ushered in the revolutionary discoveries of the

early 20th century.

Example 1

Convert 75 degrees Fahrenheit to Celsius.

Solution

To do this conversion, we’ll just use the equation given above.

Tc=

5

9

(Tf− 32 ◦F)

Tc=

5

9

( 75 ◦F− 32 ◦F)

Tc= 23. 8 ◦C

Example 2

The mass of a neon atom is 3. 34 ∗ 10 −^26 kg. If the temperature of the neon atom 100 K, what is it’s average

velocity?

Solution

We can solve this problem using the equation given above relating kinetic energy to the temperature of a gas.