AP Physics

Mr. JeanNovember 8th, 2011

Problems:

A segment of steel railroad track has a length of 30.000m when the temperature is at 0.0oC.

What is it’s length at 40.0oC?

Helpful Hint: α = 11 x 10-6(oC)-1

Solution:

Lf = Li + Le

Lf = 30.000m + 0.013m

Lf = 30.013m

Full solution on p.540 Serway & Jewett

Kinetic Theory: Temperature and pressure are macroscopic properties of

gases. These properties are related to molecular motion, which is a microscopic phenomenon. The kinetic theory of gases correlates between macroscopic properties and microscopic phenomena. Kinetics means the study of motion, and in this case motions of gas molecules.

At the same temperature and volume, the same numbers of moles of all gases exert the same pressure on the walls of their containers. This is known as Avogadros principle. His theory implies that same numbers of moles of gas have the same number of molecules.

Common sense tells us that the pressure is proportional to the average kinetic energy of all the gas molecules. Avogadros principle also implies that the kinetic energies of various gases are the same at the same temperature. The molecular masses are different from gas to gas, and if all gases have the same average kinetic energy, the average speed of a gas is unique.

Kinetic Theory:

Ideal Gas Law PV = nRT

– P = pressure– V = Volume– n = Number of moles– R = Atomic constant– T = Temperature

Thought Question

A common material for cushioning objects in packages is made by trapping Bumble’s of air between sheets of plastic. This material is more effective at keeping the contents of the package from moving around inside when.

A) On a hot day B) On a cold day C) Either hot or cold days

Question:

A spray can containing a propellant gas at twice atmospheric pressure (202 kPa) and having a volume of 125cm3 is at 22oC. It is tossed into an open fire. When the temperature reaches 195oC what is the pressure in the can?

Assume NO volume change. Assume Ideal Gas.

Solution:

Ideal Gas Law PV = nRT

No air escapes during the compression, so that ‘nR’ remain constant. Thus we can eliminate them from both sides of the equation.

PiVi = PfVf

Ti Tf

Solution:

Pf = (Tf / Ti) Pi

Pf = 320 kPa

Thought Question: In air, the molecular mass of oxygen

molecules is 32 g/mol; the molecular mass of nitrogen molecules is 28 g/mol. Which molecules are traveling faster on average?

a. Oxygenb. Nitrogenc. Same speed

Equipartition Theorem “The total kinetic energy of a system is

shared equally among all of its independent parts, on the average, once the system has reached thermal equilibrium.”

“independent”: e.g. x, y, z (for translational KE)

“parts”: translational, rotational, vibrational

Specifically, each “degree of freedom”, of each molecule, has “thermal energy” of …

½kBT

Thermal energy (measured by kBT) must be comparable to the quantum energy levels, or some degrees of freedom get “frozen out”

From section 21.4: diatomic hydrogen

Y-axis: heat added, divided by temperature change (per mole)Units: J/molK

Translational KE:

Calculate the average kinetic energy of one nitrogen molecule at 300K?

Hint: Ek = 3/2 (RT) Mr.Cooper should

have given you this equation by now.

Solution

Assume nitrogen behave as an ideal gas, then

Ek = 3/2 R T    = (3/2) 8.3145 J/(mol K) * 300 K    = 3742 J / mol (or 3.74 kJ/mol)

Molecular View of Pressure, cont.

Result for v instead of vx:

a. P = N m ⅓ v2 / V

What does PV equal?

Compare to: PV = N kB T

What does T equal?

Question:

Which “molecules” have the most kinetic energy?

a. The heavy onesb. The light onesc. Same

Which ones have the fastest average velocity?