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Kinetic Energy and Temperature

What is Kinetic Energy? All moving objects (including atoms and molecules) have a form of energy called kinetic energy. This is the energy that objects have that is due to their movement. Because there are different types of motion, there are different kinds of kinetic energy.

Types of kinetic energy include:

In this section, we will talk about the translational kinetic energy of an object. This is the kinetic energy of objects due to their movement across a distance (shown below). 



Translational kinetic energy is typically the type of kinetic energy people mean when they talk about "kinetic energy." The translational kinetic energy of an object's atoms/molecules is also the type of kinetic energy that defines the object's temperature. In this section, we will be talking about translational kinetic energy, but we will just call it "kinetic energy" here.

Mathematical definition of kinetic energy. The relationship between the kinetic energy of an object and its mass (m) and speed (or velocity, v) is shown below:

The relationship between the kinetic energy of an object and its mass (m) and speed (or velocity)



In the graph above, the relationship between mass and kinetic energy is best represented by

In the graph above, the relationship between velocity and kinetic energy is best represented by
Check your basic understanding:
Q1: What is the kinetic energy (KE) of an object that is not moving?
a) It's impossible to tell.

b) It's equal to the mass of the object.

c) Zero.

d) None of the above.


Q2: Based on the formula for kinetic energy, does an object's mass or speed/velocity have a greater effect on an object's kinetic energy?
a) Its mass.

b) Its speed/velocity.

c) Mass and speed/velocity have the same influence on kinetic energy.

d) None of the above.



Q3.1: A 60 kg (132 pound) middle school athlete can sprint at 10 m/s (about 20 mph). What is the kinetic energy of the kid?
a) 300 kg × m/s

b) 600 kg × m/s

c) 3,000 kg × m2/s2

d) 6,000 kg x m2/s2


Q3.2: A Hydrogen molecule (H2) has a mass of 2 amu. ("amu" stands for "atomic mass units", which is equal to the mass of one proton or neutron, which is 0.00000000000000000000000334 grams.) This molecule is moving around in the Earth's atmosphere at a speed of 500 m/s. What is its kinetic energy?
a) 500 amu × m/s

b) 1,000 amu × m/s

c) 250,000 amu × m2/s2

d) None of the above.


Definition of temperature. The temperature of an object is the average kinetic energy of the particles (atoms and/or molecules) that make up the object. The kinetic energy of individual particles is determined by both their speed and mass. So, the temperature of an object increases as the speed or mass of its atoms/molecules increases.

Let's say there are two containers of the same gas (e.g., helium atoms). As shown in the picture below (a microscopic view showing just a few of the millions of atoms in the containers), the helium atoms in Container 1 (below, left) are moving at about twice the average speed of the helium atoms in Container 2 (below, right). The length of the arrows represents the speed of the atoms: longer arrows mean higher speed. The direction of the arrows shows the direction of motion at that time point.


Two boxes showing helium atoms

Temperature increases as the mass of atoms/molecules increases. The temperature of an object also depends on the mass of the atoms and/or molecules that make up that object. 

Now let's say we have a container with helium atoms and a second container with argon atoms. (Again, a microscopic view of only a few of the millions of atoms in each container are shown below.) The helium atoms in Container 1 and the argon atoms in Container 3 have the same average speed.


Helium and Argon atoms

Temperature of Object = Average Kinetic Energy (1/2mv2) of all of its molecules

Check your (more advanced) understanding:
Q4: There are two glasses of water (H2O). You measure the temperature of the water in Glass 1 as 15 degrees C. You measure the temperature of the water in Glass 2 as 30 degrees C. Which of the following is true:
a) On average, the H2O molecules in Glass 1 are moving around faster than H2O molecules in Glass 2.

b) On average, the H2O molecules in Glass 2 are moving around faster than H2O molecules in Glass 1.

c) On average, the H2O in Glass 1 are moving around at the same speed as H2O in Glass 2.

d) More information is needed to answer.


Q5: A gold ring and a glass of water that are sitting on a desk are at the same temperature (room temperature). What do you think is true of the average speed of the ring's gold atoms vs. the water molecules? (Hint: look at the periodic table)
a) They are the same

b) The gold atoms move faster on average

c) The water molecules move faster on average

d) I don't know.

This simulation below shows the motion of molecules as the temperature changes. The molecules are represented as bright blue circles below. They are magnified by a lot so we can see them in this simulation.


States of Matter: Basics
Click to Run

Phet States of Matter Simulation (click above to view)