Question

In your own words, describe Charles’s Law. Express Charles’s Law as a mathematical equation. Which variable must be held constant for Charles’s Law to work?

In your own words, describe Gay-Lussac’s Law. Express Gay-Lussac’s Law as a mathematical equation. Which variable must be held constant for Gay-Lussac’s Law to work?

Answer 1

The Charles's Law states that when the temperature of a gas is increased, its volume will raise proportionally to the tempreature raise, and for this to be true, the pressure needs to be constant troughout the process. To express this in a mathematical way we have to say that:

Wich means that temperature and volume are proportional, therefore:

Where is a constant value.

according to what we defien earlier, we can say that if the volume increases as the temperature raises then the relation between the initial stage and the final stage of the cycle must be constant, Thus.

or;

The equation shows that, as absolute temperature increases, the volume of the gas also increases in proportion.

The Gay-Lussac's Law works in the same manner as the Charles's Law, but in this cases it states that when a gas's temperature increases, then so does its pressure if the mass and volume of the gas are held constant. So, in theis case, the mass and volume must be constant for the law to work.

And to express this relation mathematically we must state:

Wich means that pressure and temperature are proportional, therefore:

And in the same manner, the relationship between the initial and final stages of the process are given by:

or;

It is important to consider that Both laws are restricted to a constant value, when one is constat the other cannot be.