Question

A balloon filled with helium has a volume of 37.7 L at 299 K. What volume will the balloon occupy at 267 K?

Answer 1

This is a very straightforward application of Charles's Law. Let me state the law breifly:-

Charles Law is an empirical relation between the quantities of Volume and Tempreture for an ideal gas. The Law can be mathematically stated as:

. Implying that the Volume of a gas is directly proportional to the Tempreture of the gas.

Now we can remove the proportionality sign and state that Charles Law is equivalent to :

where the subscipts indicate the two observations of Volume and Tempreture properties of a gas.

We now just have to put in the values of V_1, T₁, and T₂.
We then get:

. (Note the bracketed (l) and (K) are just the units of the quantites.)

Solving for x gives us which gives us .

I hope this has helped. In case the answer is unclear, feel free to reach me via the comments. I will be very glad to help you out.