1.1 The First Law of Thermodynamics

Take-home message: The sum of the work done on and the heat added to a system is a function of state. It is called the internal energy.

For adiabatic changes the amount of work required to produce a given change of state is independent of the way the work is done. This suggests that the internal energy $E$ of the system is a function of state.

For non-adiabatic changes energy can also enter or leave the system as heat, and the work done is no longer independent of the process. However the sum of energy added in the form of heat and work is. This is the first law of thermodynamics:

$\mbox{\LARGE\colorbox{yellow}{\rule[-3mm]{0mm}{10mm} \ $\displaystyle \Delta E=Q+W$ }}$

Remember $Q$ is the heat added to the system and $W$ is the work done on the system (eg by compression). (Warning: if you surf the web you will come across sites written by chemists, and they use a different sign convention.)

Mancunian James Joule was a key figure in establishing the interconvertability of work and heat.

Here we have an example of two different processes which involve the same change in state. We start with an ideal gas at $(V_0,T_0)$ and in both cases the final state is $(2V_0,T_0)$.

In the first case the gas is initially confined to one half of an insulated container. When the partition is removed it fills the whole container. Here no heat is exchanged or work done, so

$$\Delta E = 0$$

Because the gas is ideal, the energy is a function of temperature only, so no change in internal energy means no change in temperature.

In the second case the temperature is held constant by a heat bath. The expansion does work against an external force, so $W<0$. However the endpoint is the same as in the previous case, so once again $\Delta E=0$. Thus there must be a flow of heat into the system:

$$Q=\Delta E - W = \vert W\vert$$

References

• Mandl 1.3
• Bowley and Sánchez 1.5
• Adkins 3.1-4
• Zemansky 4.1-6