Work

Here, we begin to relate energy and pressure together.

Energy and pressure

Pressure multiplied by volume is energy. You can see this from the ideal gas law, where pV = nRT leads to energy on both sides. So a change in pressure and volume must relate to an energy change. Providing pressure is constant, we can define a specific type of energy known as work, w.

[-pDelta V=w]

This is probably one of the stronger definitions of what energy is: energy is a quantity that can cause work to happen.

This is because changing a volume against an external pressure requires pushing against a force over a particular distance. This can either be thought of as multiplying the force by the distance moved, or integrating it over the distance if the force is not necessarily constant. Therefore force is a derivative of energy. Specifically, here, potential energy because these changes alter the configuration of the system.

[V=-int F:dx] [F=frac{dV}{dx}]

For the purpose of this course, we won’t be looking at integration and differentiation, but if you’re already aware of it, this is what is happening more precisely.

Signs – positive and negative

It’s worth noting the sign of these values – the relationship is between work and the pressure/volume change is defined as negative. This is because expansion takes energy from the system, so its energy must become lower.

Relationship to internal energy

Work done will alter the internal energy, U, of a system by changing its configuration. A system’s internal energy may also be altered by heat. Heat is the transfer of energy by microscopic collisions. Any internal energy change must be accounted for by work and heat.

This leads to the first law of thermodynamics, which is mostly a statement about conservation of energy.

[Delta U = w + q]

Note the sign here. Adding these two quantities is the convention within chemistry. You may see it written differently in other disciplines, which define the direction of heat flow and work differently depending on their needs.