# 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.**

**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!)

* 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:**

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 T_{1}.

So, T_{1} > T_{2} > T_{3}.