Gas Molecule Motion

At a low temperature a gas molecule travels, on the average, at a slower speed than than it would at a high temperature. So, at a low temperature the molecules have, on the average, less kinetic energy than they do at a high temperature. Lower speeds, lower kinetic energies. If we imagine a gas molecule as a green circle:

Molecule at low temperature has low speed and low kinetic energy molecule at high temperature has high speed with high kinetic energy

Temperature, when measured in Kelvin degrees, is a number that is directly proportional to the average kinetic energy of the molecules in a substance. So, when the molecules of a substance have a small average kinetic energy, then the temperature of the substance is low. And large average kinetic energy means the temperature is high. Remembering that the lower case Greek letter alpha (α) means 'is directly proportional to', in symbols we have:

T α KE_ave

In the following animation gas molecules are modeled as little circles. They are bouncing around in two sealed containers.

The left container shows all of the gas molecules traveling at the same speed. This is not a perfect representation of their motion. Actually, these gas molecules would all travel at different speeds, and so all have different kinetic energies.

However, for any temperature there is an average kinetic energy and a corresponding average speed for the motion of these molecules. This animation visualizes the molecules to be traveling at this average speed.

The right container works the same way, but at a higher average speed.

Lower Temperature	Higher Temperature

Click this button to see the computer code for the above animation.

Here's the code that runs the above animation.

You can change the code, if you like, and then click the following 'Reevaluate code' button. The program will then work as per your changes. Of course, your changes, especially random changes, can introduce errors, miscalculations, and browser crashes. If you need to get things back to their original condition, just reload this page using your browser's reload button.

The intention here is to conveniently show the inner workings of this program so that you understand how the diagram is drawn. Can you figure out how to change things so that the molecules move at a different speed?

Click the 'Code' button again to close this section.

// gas molecule motion

var t;  // current time
var dt; // delta time

var x1  = new Array(); // 1 is for left animation 
var y1  = new Array();
var vx1 = new Array();
var vy1 = new Array();

var xMin1 = 0;
var xMax1 = 354;
var yMin1 = 0;
var yMax1 = 212;

var x2  = new Array(); // 2 is for right animation
var y2  = new Array();
var vx2 = new Array();
var vy2 = new Array();

var xMin2 = 0;
var xMax2 = 500;
var yMin2 = 0;
var yMax2 = 300;

var loopWait = 50; // milliseconds

var twoPi = 2 * Math.PI;

var numPoints = 100; // number of gas molecules


setup = function()
{
	var randomX1Min = 10;  // minimums and maximums
	var randomX1Max = 334; // for random positions
	var randomY1Min = 10;
	var randomY1Max = 192; 
	var randomX2Min = 10;
	var randomX2Max = 490;
	var randomY2Min = 10;
	var randomY2Max = 290; 
	
	var v1 = 20.00; // velocity for slow molecules
	var v2 = 28.28; // velocity for fast molecules
	
	var angle; // direction of a molecule
	
	// initialize positions and velocities
	for(var i = 0; i < numPoints; i++)
	{
		// random initial positions
		x1[i] = randomX1Min + Math.random() * randomX1Max;
		y1[i] = randomY1Min + Math.random() * randomY1Max;
		
		x2[i] = randomX2Min + Math.random() * randomX2Max;
		y2[i] = randomY2Min + Math.random() * randomY2Max;
		
		// random initial velocities
		angle = Math.random() * twoPi; // random direction
		vx1[i] = v1 * Math.cos(angle); // x-component of velocity
		vy1[i] = v1 * Math.sin(angle); // y-component of velocity
		
		angle = Math.random() * twoPi;
		vx2[i] = v2 * Math.cos(angle);
		vy2[i] = v2 * Math.sin(angle);
	}
	
	// initialize time
	t  = 0;
	dt = 0.1;
	
	// animation graphics setup
	canvas1GC.strokeStyle = 'lime';
	canvas2GC.strokeStyle = 'lime';
	
	canvas1GC.lineWidth = 2;
	canvas2GC.lineWidth = 2;
};


loop = function()
{
	// move all the molecules to their new positions
	update();
	
	// draw all the molecules at their new positions
	render();
	
	// wait a bit, then do this again
	loopTimeout = setTimeout(loop, loopWait);
};


update = function()
{
	// advance particles
	for(var i = 0; i < numPoints; i++)
	{
		// new position equals old position
		// plus velocity times delta time
		x1[i] = x1[i] + vx1[i] * dt;
		y1[i] = y1[i] + vy1[i] * dt;
		x2[i] = x2[i] + vx2[i] * dt;
		y2[i] = y2[i] + vy2[i] * dt;
	
		// bounce particles
		// check the x-coordinate for 1
		if(x1[i] < xMin1) // if out of bounds on left
		{
			// reposition molecule inside bounds
			// this method works for non-accelerated motion
			x1[i] = (2 * xMin1) - x1[i];
		
			// reverse the velocity
			vx1[i] *= -1;
		}
		else if(x1[i] > xMax1) // if not out of left bound, maybe right
		{		
			x1[i] = (2 * xMax1) - x1[i];
		
			vx1[i] *= -1;
		}
		
		// check the y-coordinate for 1
		if(y1[i] < yMin1)
		{		
			y1[i] = (2 * yMin1) - y1[i];
		
			vy1[i] *= -1;
		}
		else if(y1[i] > yMax1)
		{		
			y1[i] = (2 * yMax1) - y1[i];
		
			vy1[i] *= -1;
		}
		
		// check the x-coordinate for 2
		if(x2[i] < xMin2)
		{		
			x2[i] = (2 * xMin2) - x2[i];
		
			vx2[i] *= -1;
		}
		else if(x2[i] > xMax2)
		{		
			x2[i] = (2 * xMax2) - x2[i];
		
			vx2[i] *= -1;
		}
		
		// check the y-coordinate for 2
		if(y2[i] < yMin2)
		{		
			y2[i] = (2 * yMin2) - y2[i];
		
			vy2[i] *= -1;
		}
		else if(y2[i] > yMax2)
		{		
			y2[i] = (2 * yMax2) - y2[i];
		
			vy2[i] *= -1;
		}
	}
};


render = function()
{
	// erase the old picture
	canvas1GC.clearRect(0, 0, xMax1, yMax1);
	canvas2GC.clearRect(0, 0, xMax2, yMax2);
	
	// draw the new picture
	for(var i = 0; i < numPoints; i++)
	{
		// draw a molecule on 1
		canvas1GC.beginPath();
		canvas1GC.arc(x1[i], y1[i], 5, 0, twoPi);
		canvas1GC.closePath();
		canvas1GC.stroke();

		// draw a molecule on 2
		canvas2GC.beginPath();
		canvas2GC.arc(x2[i], y2[i], 5, 0, twoPi);
		canvas2GC.closePath();
		canvas2GC.stroke();
	}
};

The right container's molecules are at a higher temperature than those on the left. Compare their speeds carefully. The ones on the right are faster. These are faster by a factor of the square root of two, 1.414. This makes the average kinetic energy of these molecules to be twice that of those to the right, since the kinetic energy of a body is proportional to the square of the speed of the body. Consequently, this right container represents a gas at twice the Kelvin temperature than the gas in the container on the left.

The area of the right container (higher temperature) is twice as large as the area of the left container (lower container) so that the pressure of the gas is properly simulated as being equal in both. This allows us to properly visualize the effect of a temperature change on the speed of gas molecules without concerns about other effects due to pressure changes.

What you should notice in the right container is that the higher temperature is tied to a higher average speed. This results in the molecules having a higher average kinetic energy.

In the right container there is an increase in the kinetic energies of the molecules due to an input of heat. Why are those molecules on the right going faster than those on the left? Well, we could imagine that they were once going the same speed as those on the left and then they received an input of heat (energy). After the heat input, they move faster.

Heat, as stated earlier, is energy. If the kinetic energies of the molecules go up, then the heat (energy) within the gas has gone up. Therefore, we see an input of heat can cause an increase in temperature because the input of heat is realized as an increase in the kinetic energies of the gas molecules. When the average kinetic energy of the gas molecules goes up, the temperature goes up. Heat goes into a substance, the temperature goes up - that's one way it can work.

An input of heat is not always accompanied by an increase in temperature, however. That is very important to understand. The heat (energy) could be used to change the bonding between the molecules rather than be used to speed up the molecules. This would be a situation where heat goes into a substance, and the temperature does not rise, as when ice melts or water boils. In these cases the increase in heat (energy) is used to change bonding between the molecules rather than change their kinetic energies.

Lower Temperature

Higher Temperature