we saw in the last video that pressure in gases is caused by gas particles colliding with the walls of the container and that we can increase the pressure by increasing the temperature increasing the number of particles or decreasing the volume this last rule means that pressure and volume are inversely related so as one goes up the other goes down this means that for a given amount of gas at a constant temperature the pressure times the volume will always be a constant value which is how we get our pv equals constant equation for example if we increased the volume then the pressure would decrease so when multiplied together let's still give the same value regardless of why this works though all we need to be able to do is use it in calculations so let's give it a go and try a couple of examples an unknown gas occupies a volume of 1.5 meters cubed at a pressure of 100 pascals calculate the pressure exerted by the gas if it's compressed to a volume of 0.3 meters cubed assume that the temperature and mass of the gas stayed the same so with questions like this it's helpful to write out what we have effectively we've got 1.5 meters cubed of a gas with a pressure of 100 pascals and then 0.3 meters cubed of gas with an unknown pressure which is what we're trying to find so if we take our equation pv equals constant we can figure out the constant for the first gas sample by taking the pressure of 100 pascals and multiplying it by the volume of 1.5 meters cubed which gives us a constant of 150 then looking at our other gas sample we know that its pressure times its volume must also equal 150 so to find the pressure we just plug in the 0.3 and then rearrange by dividing both sides by 0.3 which gives us 500 pascals so we know that this new container must be at a pressure of 500 pascals now there is another way of doing this that some people prefer because the constant is the same for both containers instead of actually figuring out the constant we can just say that the pressure times the volume in the first container equals the pressure times the volume in the second container and to avoid getting the numbers confused we normally say that p1 times v1 equals p2 times v2 so 100 times 1.5 equals something times 0.3 which we can rearrange to get 500 past scales just like we got before let's try one more to prepare for a dive eighteen hundred liters of air from the atmosphere is compressed into a twelve liter gas cylinder calculate the pressure of the air in the cylinder assume that the temperature remains constant and that atmospheric pressure is 101 kilopascals in this question it's a bit more difficult to see which values we're meant to use where we're basically taking a volume of 1800 liters of atmospheric air and compressing it into the much smaller volume of 12 liters at an unknown pressure the key thing to notice though is that atmospheric air will have a pressure of 101 kilopascals so if we take the equation we just mentioned all we have to do is substitute in 101 times hundred which will equal something times twelve then we just divide both sides by twelve and that'll give us a pressure of fifteen thousand one hundred and fifty and importantly that will be in the units of kilopascals as we used kilopascals for the units of our atmospheric gas anyway that's all for this video so hope you found it useful and we'll see you next time