# The First Law of Thermaodynamics

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## The First Law of Thermaodynamics

Imagine a balloon full of gas!

There are only 2 ways that you can change the internal energy, U of the gas. (without adding or removing any atoms).

**Heat it or cool it**i.e. ΔQ or**heat transferred.****Compress it or expand it**i.e. ΔW or**work done**.

(See note in section above about **internal energy**)

This leads us to the **first law of Thermodynamics** but first let's just look at the two more closely.

**Heat**

If you heat up gas, you pass energy to the atoms. (It appears as E_{k}).

**Heat flowing into the gas is positive.**

**Work**

If gas expands it has to push back the stuff that was around it. It has to do work (use energy) to do this. This is related to its internal energy.

**We define work done by the gas pushing back its surroundings as positive.**

**Equation for work done by a gas.**

We can actually calculate how much work gas has to do to push back its surroundings

In this cylinder with a frictionless piston (of area, A) the gas is at pressure P. If it expands and pushes back the piston by a very small distance, **x** (so small that pressure doesn't change) we can work out energy used.

**W= F x s**

and the force is provided by pressure on area A so

**F = P x A**

**Therefore**

**W = P.A.s**

* Note*: A.s = the change of volume due to expansion = ΔV

So **W = PΔV**

The **First Law of Thermodynamics** explains the energy changes that occur when you do things to a gas sample.

**In words:**

The change in internal energy of the gas sample = amount of heat energy passed to / from gas - the work done on / by gas.

ΔU = ΔQ - ΔW

or

ΔQ = ΔU + ΔW

* Note*: the negative sign (in the top version of the equation) is slightly confusing but it's due to the fact that we have said work done

**by**gas is positive. If we'd said work done

**on**gas positive this would be a + sign BUT the equation would give more confusing answers in several other situations so, trust me - stick with this!!

**For constant pressure processes use:**

ΔU = ΔQ - pΔV