 # Gay-Lussac's Law Practice Problems (part 2) okay here's our last problem this is this is for any paintball enthusiast so who enjoy playing paintball out there all right in the morning a paintball pressure tank is at 306 atm if you play paintball this is about 4500 psi what those like really fancy high-pressure paintball tanks can hold all right the weather heats up over the course of the day and by 3:00 p.m. the outside temperature is roasting at 38.5 degrees Celsius whoo that is hot that's about little over 100 degrees Fahrenheit and the pressure inside the tank has gone up to 324 atm what was the temperature in degrees Celsius in the morning okay so just as before let's go through here and look at our variables okay we're dealing with a change in the morning the paintball tank is a low-pressure heats up the pressure gets higher okay so in the morning paintball pressure tank is at 306 atm so initial pressure p1 is 306 atm the weather heats up over the course of the day so there's our change and by 3:00 p.m.
the outside temperature is second temperature 38.5 degrees Celsius you may already be thinking up we got to convert that to Kelvin you're exactly right we'll come back and do that in a minute okay and the pressure inside so p2 the pressure after the change is 324 atm what was the temperature in the morning so what was the initial temperature that's our variable we know P 1 we know P 2 we knew no t2 and we're going to be solving for T 1 all right now just again we've got to convert the Celsius temperature into a Calvin temperature before we can before we can continue alright so just as we've done before t2 is going to be 273 plus 38.5 and when I do the math I'm get 311 0.5 but remember significant figures when we're adding this one has a decimal place this one doesn't which means we draw a line right here and then we look at from this one to the right here do we round up or do we keep it the same well it's a 5 so we round up so it's going to
be 312 Kelvin is going to be 312 Calvin is going to be our t2 okay so now we can go ahead and we can solve for t1 but I told you I was going to show you a quick way to do it all right here's how we do this normally it's in the denominator so take a bunch of steps to get it on one side and get it alone okay what I'm going to do here is I'm going to use cross multiplication you may have done this in your math classes before but what it means is that this times this is equal to this times this so I can write t1 times p2 equals p1 times t2 alright most of my work is already done because I've gotten this guy a hold of the denominator now all I have to do is go from here to get it by itself so what I'll do is I'll take this and I'll divide both sides by P 2 so T 1 will be all by itself and we'll be ready to go okay p2 on top P 2 on the bottom that means they cancel out and I can rewrite this equation as t1 equals p1 times t2 divided by p2 all right
we're set we're ready to go let's plug in these numbers now p1 306 ATM times t2 312 Kelvin divided by p2 324 ATM I'm going to do the math how many numbers am I going to round my answer to I'm going to round my answer to 3 because there are three significant digits in each of these each of these numbers here so my final answer is going to be 295 Kelvin but the question asked what was the temperature what was the initial temperature in the morning all right so I'm going to
have to go back and take my kelvin temperature subtract 273 to get my Celsius temperature okay so my T 1 is going to equal to 95 minus 273 that's going to be 22 degrees Celsius and that is my final answer and that is how we can solve gas law

using gay

's law