Kinetic Energy of Gases

now kinetic energy is the energy and object possesses due to its motion. And since we're looking at gas is we're gonna look at how we can use the kinetic energy formulas and relate them to the motion of gas is so here we're gonna say we have two different versions in the first one. We use this one. We have the mass and velocity of a gas. Here we say kinetic energy abbreviated as K e equals half m times V squared here. We're going to say that M is the mass of the gas in kilograms here. It's not a mass in grams, it's in kilograms and V equals velocity of the gas in meters per second. Now kinetic energy, the the value of that will be in jewels or if we take a look, this is in kilograms and and velocities meters over seconds. Right. But it's being squared. So that would mean when we multiply kilograms times, meters over second and all that's being squared, that comes out 2 kg times meters squared over seconds squared. So here jewels are equivalent to kilograms times meter squared over second squared. Now going on the other side. We use this version when we have the moles and temperature of a gas. In this version, we're gonna say kinetic energy now equals 3/2. And then we have times, moles, times rt here and equals the amount of gas in moles are remember we use 8.314 when we're talking about velocity, speed or energy Here we're talking about kinetic energy, so we're using 8.314 Temperature equals this always in units of Kelvin. And then we're going to say here, when we're multiplying these values out, we get leaders, times, atmospheres as the units, and that's an equal to one a 1.3 to jewels. Now, here we have these two kinetic formulas realize that neither one is in purple boxes, which means you don't need to memorize them. If you'll be asked to deal with kinetic energy in some way, you tend to see it embedded within the question or on a formula shoot. Just keep in mind based on if you're dealing with mass and velocity, use the one on the left and if you're dealing with moles and temperature, he used the one on the right

So here we're told that a 1.56 times 10 to the 13 PICO Graham gashes Particle travels at 6.21 m per second determine its kinetic energy. So here were given the mass of the gashes particle and its velocity. Because we're giving mass and velocity, we have to use the kinetic energy on the left side. So kinetic energy equals half times mass times velocity squared. Remember, your mass has to be in kilograms, so we're gonna have to do a metric prefix conversion. So we're gonna change PICO Grams first into grams and remember that a PICO one PICO is 10 to the negative and then finally we're gonna go from grams to kilograms. 1 kg is tend to the three. When we do that, we're going to get 1.56 times 10 to the negative, 2 kg, So that's gonna go in for my mass. So this equals half times times 10 to the negative 2 kg. My velocity is already in meters per second, so no need to convert anything. This whole thing is going to be squared. So that's really half times 1. times, 10 to the negative. 2 kg. When I square everything inside of here that comes out to 38.5641 m squared over seconds squared. So then here, when we multiply everything out multiplied by half is well. That comes out to 6.2 times 10 to the minus 1 kg times meter squared over second squared, which is equivalent to Jules. Okay, so we could just simply say that it's 6.2 times 10 to the negative one jewels. So just remember, in this one for kinetic energy were given mass and velocity, so it's just equal to half times mass times velocity squared.