00:01
In this problem, we have an ideal gas, and for that ideal gas, we are given a value of pressure, our volume, and our velocity.
00:14
And so we are asked if pressure and volume and volume are increased by three times the amount, what is our velocity? and so initially, with what we're given in the problem, let's go ahead and write down our equation for kinetic energy for an ideal gas molecule.
00:58
And so what the equation is, three halves kt, or k is the boltzman constant, and this is also equal to three halves pressure times volume.
01:15
And so i'm gonna call this for our case one, which is the case one in which the pressure and volume are kept at our given problem statement conditions.
01:26
And so in our case 2, where our pressure and volume are increased by three times the amount, i'm going to call that kinetic energy, k -e -2.
01:37
And so if we plug in our values, we are going to represent our, again, 3 -5s k -t, and our 3 -2 will be equal to 3 -2.
01:53
And for our pressure component, which we put just p in our k -e -1 equation, this will be equal to 3p, and our volume will be equal to three times the volume.
02:08
And so now what we can do is focus on these expressions for kinetic energy in terms of pressure and volume.
02:18
And so let's go ahead and assess the ratio from our kinetic energy 2 to our kinetic energy 1.
02:26
So if we write down, rewrite down our expressions here.
02:31
You have three halves times three p times three v over our three halves times p.
02:48
And so let's see what we can cancel out in this ratio express.
02:53
So our three halves can cross off, we can cross off corresponding p, p, and the volume term.
03:01
So when we get this ratio, we get a ratio of 9...