Video Transcript
For a gas at a constant volume, if the temperature is blank, then the pressure blank. Option one: decreased, increases; option two: decreased, stays the same; option three: increased, increases; option four: increased, decreases; or option five: increased, stays the same.
Now, this is a fill in the blank kind of question and we need to pick the option that gives us the correct words to put into these blanks here. So first things first, we know that the gas is at a constant volume. And in this question, we’re comparing the temperature of the gas and the pressure of the gas.
So in order to be able to answer this question, we need to use what’s known as Gay–Lussac’s law. This law says that for a gas at a constant volume 𝑉, the pressure of the gas is directly proportional to the temperature. And this only applies when the gas is at a constant volume. Luckily for us, we’re told that it is in the question the gas is at a constant volume.
So for this gas, the pressure must be directly proportional to the temperature. In other words, if the pressure increases, then the temperature will also increase. If the pressure decreases, then the temperature will also decrease. And if the pressure stays the same, then the temperature stays the same. So we need to find the one option out of one, two, three, four, and five that reflects this direct proportionality relationship.
Remember the first words in each of these options are meant to fill the first blank, which is this one here. And the second words are meant to fill the second blank, which is this one.
So let’s go through option one. If the temperature is decreased, then the pressure increases. In other words, a temperature increase results in a pressure decrease. Well, that’s not one of these options here. So number one is not what we’re looking for. Number two: if the temperature is decreased, then the pressure stays the same. Again, not one of the options, so number two is out of the question.
Number three: if the temperature is increased, then the pressure increases. Yes, that does reflect the direct proportionality relationship. So it looks like number three is our answer. But let’s go through numbers four and five just in case. Number four: if the temperature is increased, then the pressure decreases — once again not correct. And number five: if the temperature is increased, then the pressure stays the same — as we expected, incorrect.
And so it looks like we have our answer. For a gas at a constant volume, if the temperature is increased, then the pressure increases.
