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).

  1. Heat it or cool it i.e. ΔQ or heat transferred.

  2. 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.


If you heat up gas, you pass energy to the atoms. (It appears as Ek).

Heat flowing into the gas is positive.


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

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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


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


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

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