Thermal physics confusion

Hi,
Due to my lack of revision on this topic, I have had difficulty understanding this graph. The mark scheme states that the work done is the pressure multiplied by the volume (area under the curve). Very confused on how this is derived, have I missed something obvious?

Another thing that I am confused about is that Save My Exams says that this is only true for constant pressure (W=pΔV), but the mark scheme says that I can work out the difference in work done by finding the area under the curve, where the pressure is changing constantly.

I have attached images and written the question on the first one :smile:

Would really appreciate some explanation if someone has time to do so.

Screenshot 2024-05-27 153835.png

Reply 1

mosaurlodon

The way its derived is Work done = Force * distance
Pressure = Force/Area
Volume = Area * distance
so Pressure * Volume = Force * distance (as Area cancels) = Work done

Work done is always the area under a graph of pressure against volume
For the Save My Exams part, you can imagine a rectangle in the graph where there is constant pressure of b and volume changes from 0 to a.
In this case there is constant pressure and you can use the equation Work done = Pressure * Volume
= a*b (which is the same as working out the area under the graph as the rectangle has height b and width a)
When the shape isnt a rectangle (i.e. the pressure is not constant) you can simply work out the area under the graph and this will get you work done.

Its the same reasoning for how speed*time = distance but only if speed is constant.
If speed is not constant the distance is just the area of the speed-time graph.