03.2b - Kinetic Molecular Theory

In the simulation below, the initial state of the molecules can be changed by dragging them to different locations (changing the potential energy btwn them). The two molecules that are initially in motion can also be adjusted.

What questions do you have when observing the molecules interacting?

Inject both Heavy and Light molecules into the chamber:

Compare their Speeds and Kinetic Energy.

KMT in Molecules

In the diagram to the right, the 5 molecules can be consider ideal gas molecules, each with mass m. They are bound by the container.

Which of the molecules has the greatest kinetic energy? the molecule with a velocity of 10m/s
In terms of m, determine the total internal energy of the system. ΣKE of all molecules: 140m J.
In terms of m, determine the average kinetic energy of the system. 28m J/molecule
Suppose 560 Joules of work was done on the system (by heating), in terms of the average kinetic energy, describe the effect of the work on the temperature of the system. 140m J/ molecule

KMT Concepts

Using the KMT, explain how a fish tank (40L) of 20 C water can have more energy than a cup (200 mL) of boiling (100C) water.

Two cups are placed in a microwave oven for 5 min: (a) a 80-ml (double espresso) cup of 20 C water and (b) a 230-ml (latte) cup of 20 C water. Assume both cups are made of the same material and do not change temperature.

Which cup of water would have a greater change in temperature (average kinetic energy)? 80-ml cup - Greater change in KE / molecule
Which cup of water would have a greater change in heat (internal energy)? Both equal

KMT Equation

KMT IB Equations

The total internal energy of a system is the average kinetic energy times the number of particles.

The average kinetic energy per molecule (J/molecule) of a system is directly proportional to the temperature (K) of the system.

The derivation of this equation is not within the scope of the IB Curriculum, however, you can find an explanation here.

Keys to KMT Probs:

UNITS! UNITS! UNITS!
Working with Exponents.
1. Use the EE button.
Organization of Data. (see #3 below)

KMT Video Notes:

Who is Boltzmann and what is his constant?

KMT Problem Solving

Problems from the video:

The temperature of Argon gas (atomic wt = 40 g/mol) is 300K. Determine the average velocity of each particle of gas. v = 453m/s
The average kinetic energy of a gas is 9.32x10-20 J. What is the temperature in˚C? T = 4230˚C
Helium gas (He) is contained in a volume of 9.32x10-4 m-3 at a temperature of 300K and a pressure of 5x10-5 Pa. Calculate in J the total internal energy (Eint) of the gas. Eint) = 262J

KMT Practice Problems

2016_Topic_3_Problems_3.2.pdf

Questions 17-21 are specific to KMT. Solutions HERE

IB MC Q: The Kelvin temperature of an ideal gas is a measure of the

A. average speed of the molecules.

B. average momentum of the molecules.

C. average kinetic energy of the molecules. correct

D. average potential energy of the molecules.

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