# p-V or Indicator diagrams

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## p-V or Indicator diagrams

#### p-V or Indicator diagrams

We sketch graphs showing how pressure and volume vary when we do certain things to a gas.

Here are the four you need to understand.

Constant pressure (isobaric) process.

Note: if W = pΔV then the area below the line = work done.

Of course, ΔQ = ΔU + ΔW applies.

Constant volume (isovolumetric) process.

Note: if W = area under line then W = 0 here (confirmed by W = pΔV and ΔV = 0)

So U = Q - W becomes U = Q i.e. all heat added goes straight to internal energy.

Constant temperature (isothermal) process.

There is a change in volume so ΔW ≠ 0.

But in fact in this case, ΔU = 0.

Imagine you pass 100 J of heat to a sample but on receiving it, it expands and does 100J of work pushing back the surroundings. Overall it has gained zero joules.

So

(Told you it was useful to have a negative sign in the equation!)

Note: temperature increases, pressure increases and volume reduces, so none of these is unchanged. So why is this special?

Well in the processes that we've looked at so far we've had U = O and W = O but not Q = O. Well, this is it. In an adiabatic process → Q = O!!

What does that mean? No heat can be transferred to or from the gas!!

This happens if a process takes place very quickly so that there's no time for heat to leave. So there is always a temperature change (increase or decrease) in an adiabatic process.

Indicator diagrams look like this:

Although it is easy to read changes in p and V from the graph - you need to know that temperature can be shown on these graphs too.

The dotted lines are isothermals (lines of constant temperature). The coolest of the isothermals is T1.

So, T1 > T2 > T3.