00:01
Hey, in this question we're given the ideal gas law which states that the pressure times volume is equal to k times temperature where k is some constant.
00:12
It's not really important.
00:14
What we're going to really be focusing on is the calculus here or some part of calculus here.
00:20
Basically we're going to just be doing calculus using this equation.
00:24
So we don't really care too much about what the variables mean.
00:28
But the first question is to find dp dv.
00:32
So the way that we do this is we take the derivative with respect to v of this equation.
00:41
So now we treat p as a function of v and t as a function of v.
00:50
Hey, in this question we're given the ideal gas law which states that the pressure times volume is equal to k times or sorry we'll treat t as a constant and k of course is a constant.
01:03
So if you remember implicit differentiation this is going to be dp dv times v plus p times the derivative of v with respect to v which is one.
01:23
And then the right hand side is just going to be equal to zero.
01:27
So solving for dp dv we get dp dv is equal to negative p over v...