p-V or Indicator diagrams

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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.

Combinations of Resistors

Constant pressure (isobaric) process.

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

Of course, ΔQ = ΔU + ΔW applies.

p-V or Indicator diagrams

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.

p-V or Indicator diagrams

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.


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

p-V or Indicator diagrams

Adiabatic process..

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:

p-V or Indicator diagrams

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.

p-V or Indicator diagrams

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

So, T1 > T2 > T3.

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