Charles' Law

2.11.01 : Please note - The volume V is inversely proportional to the density (ro). Therefore the expression of the temperature multiplied by the density which we used in class, can be replaced by an expression where the temperature is divided by the specific volume. This will be further discussed in class.

Discovered by Joseph Louis Gay-Lussac (the uppermost GIF [24K] to the right) in 1802. He made reference in his paper to unpublished work done by Jacques Charles (the lower GIF [20K] to the right) about 1787. Charles had found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to the same extent over the same 80 degree interval.

Charles did invent the hydrogen-filled balloon and on December 1, 1783, he ascended into the air and became possibly the first man in history to witness a double sunset.

Gay-Lussac was no slouch in the area of ballooning. On September 16, 1804, he ascended to an altitude of 7016 meters (just over 23,000 feet - about 4.3 miles). This remained the world altitude record for almost 50 years and then was broken by only a few meters. His GIF is from a stamp France issued in memory of the 100th anniversary of his death in 1950.

Because of Gay-Lussac's reference to Charles' work, many people have come to call the law by the name of Charles' Law. There are some books which call the temperature-volume relationship by the name of Gay-Lussac's Law and there are some which call it the Law of Charles and Gay-Lussac. Needless to say, there are some confused people out there. Most textbooks call it Charles' Law.

The same year a 23-year-old Gay-Lussac discovered this law, he had occasion to walk into a linen draper's shop in Paris and there he made a wonderous discovery. He found the 17-year-old show girl reading a chemistry textbook while waiting for customers. Needless to say, he was intrigued by this and made more visits to the shop. In 1808, he and Josephine were married and over the years, five little Gay-Lussac ankle-biters were added to the scene.

This law gives the relationship between volume and temperature if pressure and amount are held constant.

If the temperature of a container is increased, the volume increases.

If the temperature of a container is decreased, the volume decreases.

Why?

Suppose the temperature is increased. This means gas molecules will move faster and they will impact the container walls more often. This means the gas pressure inside the container will increase (but only for an instant. Think of a short span of time. So there.). The greater pressure on the inside of the container walls will push them outward, thus increasing the volume. When this happens, the gas molecules will now have farther to go, thereby lowering the number of impacts and dropping the pressure back to its constant value.

It is important to note that this momentary increase in pressure lasts for only a very, very small fraction of a second. You would need a very fast, accurate pressure sensing device to measure this momentary change.

Charles' Law is a direct mathematical relationship. This means there are two connected values and when one goes up, the other also increases.

The mathematical form of Charles' Law is: T ÷ V = k

This means that the temperature-volume fraction will always be the same value if the pressure and amount remain constant.

Let T₁ and V₁ be a temperature-volume pair of data at the start of an experiment. If the temperature is changed to a new value called T₂, then the volume will change to V₂.

The new temperature-volume data pair will preserve the value of k. We do not care what the actual value of k is, only that two different temperature-volume data pairs equal the same value and that value is called k.

So we know this: T₁ ÷ V₁ = k

And we know this: T₂ ÷ V₂ = k

Since k = k, we can conclude that T₁ ÷ V₁ = T₂ ÷ V₂.

This equation of T₁ ÷ V₁ = T₂ ÷ V₂ will be very helpful in solving Charles' Law problems.

This graphic simply restates the above in a way HTML cannot do.

Notice that the right-hand equation results from cross-multiplying the first one. Some people remember one better than the other, so both are provided.

Before going to some sample problems, let's be very clear:

EVERY TEMPERATURE USED IN A CALCULATION MUST BE IN KELVINS, NOT DEGREES CELSIUS.

DON'T YOU DARE USE CELSIUS IN A NUMERICAL CALCULATION. USE KELVIN EVERY TIME.

Now, please don't send me e-mail asking me what I meant by that. Thanks.

Example #1: A gas is collected and found to fill 2.85 L at 25.0°C. What will be its volume at standard temperature?

Answer: convert 25.0°C to Kelvin and you get 298 K. Standard temperature is 273 K. We plug into our equation like this:

Remember that you have to plug into the equation in a very specific way. The temperatures and volumes come in connected pairs and you must put them in the proper place.

Example #2: 4.40 L of a gas is collected at 50.0°C. What will be its volume upon cooling to 25.0°C?

First of all, 2.20 L is the wrong answer. Sometimes a student will look at the temperature being cut in half and reason that the volume must also be cut in half. That would be true if the temperature was in Kelvin. However, in this problem the Celsius is cut in half, not the Kelvin.

Answer: convert 50.0°C to 323 K and 25.0°C to 298 K. Then plug into the equation and solve for x, like this:

Example #3: 5.00 L of a gas is collected at 100 K and then allowed to expand to 20.0 L. What must the new temperature be in order to maintain the same pressure (as required by Charles' Law)?

Answer: