00:01
We'd like to find the final temperature and the mass of the air that enters the balloon.
00:05
So let's first begin by applying our ideal gas equation.
00:10
We have pressure 1, volume 1, is equal to m, r, temperature 1.
00:15
We can plug in our pressure 1 200 times v1 equal to 0 .5 times .287 times 303 is our temperature.
00:25
So v1 is 0217 meters cubed.
00:29
But here, pressure is proportional to a diameter of a balloon.
00:36
Pressure is some constant times our diameter.
00:39
And our diameter is kv to the one -third power, where v is our volume.
00:46
So plugging in this into our diameter, we find p -1 is equal to c v -1 -3 power.
00:54
So we can plug in 200 equal to c to the 0 .217 to the 1 -3 power to find c.
01:02
We find c to be 332 .6.
01:06
Now our final volume is double our initial volume, so v2 is 2 times v1 or 0 .434 meters cubed.
01:15
We want to find the final temperature and the mass of the air.
01:21
Okay, so we have our final volume...