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Gay-Lussac's Law Practice Problems (part 2)

Feb 22, 2020
Well, here's our last problem. This is for any paintball enthusiast, so they enjoy playing paintball. In the morning, the paintball pressure tank is at 306 atm. If you play paintball, this is about 4500 psi, which those like high pressure. Paintball tanks can hold up well, the weather warms up throughout the day and by 3:00 p.m. The temperature outside is 38.5 degrees Celsius, how hot, that's just over 100 degrees Fahrenheit and the pressure inside the tank has risen to 324 atm, what was the temperature in degrees Celsius in the morning? Okay, so, as before, let's continue. here and look at our variables, okay, we are dealing with a change in the morning, the paintball tank is low pressure, it heats up, the pressure increases, okay, so in the morning the paintball pressure tank is at 306 atm , so the initial pressure p1 is 306 atm. the weather warms up throughout the day so there's our change and at 3:00 p.m. the outside temperature is the second temperature, 38.5 degrees Celsius, you might already be thinking we need to convert that to Kelvin, you're absolutely right, we'll come back and do that in a minute, okay, and the internal pressure, 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 didn't know t2 and we're going to solve for T 1 right now, again we have We have to convert the Celsius temperature into a temperature Calvin before we can continue, so just like we did before, t2 will be 273 plus 38.5 and when I do the math I get 311 0.5, but remember the significant figures. when we add this one has a decimal place, this one doesn't, which means we draw a line here and then look from this one to the right here, do we round up or keep it the same?
gay lussac s law practice problems part 2
Well, it's a 5, so we round it up so it's 312 Kelvin, it's going to be 312 Calvin is going to be our t2, okay, now we can go ahead and solve for t1, but I told you I was going to show you a quick way. To do it all right, this is how we normally do it, it's in the denominator, so it takes several steps to put it on one side and do it by itself. Well, what I'm going to do here is use cross multiplication. You may have done this in your math classes before, but what it means is that this multiplied by this equals this multiplied by this, so I can write t1 times p2 equals p1 times t2, well, for the most

part

of my work is already done because I got this guy.
gay lussac s law practice problems part 2

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Keeping the denominator now all I have to do is go from here to get it by itself, so what I'm going to do is take this and I'm going to divide both sides by P 2 so that T 1 is left alone. and we'll be ready to go, okay, p2 at the top P 2 at the bottom, that means they cancel and I can rewrite this equation as t1 is equal to p1 times t2 divided by p2, okay, we're ready, we're ready to start. Enter these numbers now p1 306 ATM multiplied by t2 312 Kelvin divided by p2 324 ATM I'm going to do the math.
gay lussac s law practice problems part 2
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 was what was the temperature, what was the initial temperature in the morning, so I'm going to have to go back and take my kelvin temperature, subtract 273 to get my Celsius temperature, so my T 1 will be equal to 95 minus 273, that will be 22 degrees Celsius and that's my final answer and that's how we can solve the gas law

problems

using Gay Lussac. law
gay lussac s law practice problems part 2

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