# Introduction to thermodynamics

Thermochemistry, the study of heat and energy and its effects on chemical reactions and physical transformations is one of the first branches of the chemical sciences and took off in the 1780s.

In chemistry, we look at how systems change when we change the conditions they are in. In terms of thermodynamics, we want to know what happens to the energy of a system under certain conditions.

Two types of energy we concern ourselves with in this area are work and heat. They are related to one another, and can be transformed from one to another. For example, heat energy released by the combustion of fuel can be used to turn a turbine, or rubbing sticks together will heat them up.

Work (w):

In physics, work is defined as

w= F x d

where F is the force exerted and d is the distance moved. In chemistry we change the equation slightly. We are no longer talking about something moving in one dimension, but a three dimensional system, we change Δd to ΔV and the force being exerted is the pressure of the gas. Therefore, work becomes:

w= -PΔV

It is negative because in chemistry we define work as that done by the system, not on it.

Heat (q):

Heat energy is related to the motion of the molecules – the hotter it is the faster they move, and jiggle about. We measure changes in heat energy by looking at changes in temperature, and the two are related via the heat capacity of the substance. The heat capacity is the amount of energy required to raise one unit of the substance by one K (or °C). Molar heat capacity is measured in J/mol.K and specific heat capacity is J/g.K.

q = CΔT

Internal energy (ΔU):

The total internal energy of the system is the sum of the potential energy and the kinetic energy. In this case, the potential energy is the work energy, and kinetic is related to the heat energy:

ΔU = w + q

Enthalpy (ΔH):

Enthalpy is a bit weird. It is the internal energy of a reaction plus any work it needs to do against the constant pressure of the atmosphere. My analogy is to imagine there is a magician who is going to make a rabbit appear: In order to create the rabbit, (assuming he is actually magical and not just concealing one in his hat), he has to use a certain amount of energy, (internal energy of a rabbit). Next, he needs to create enough space for the rabbit to appear into, so he needs to exert some work to push back the atmosphere in the rabbit-shaped space (work). The enthalpy is the total energy expended by our magician:

ΔH = ΔU +PΔV

Or

Energy expended by magician = internal energy of a rabbit + work to move the atmosphere

The real trick to understanding how these things fit together, is to look at what happens under certain circumstances:

Constant temperature:

Under constant temperature, ΔT = 0. That is fairly self-explanatory. If there is no change in temperature, then the internal energy of the system is constant, ΔU= 0, so q = w. In other words, any change in heat energy is exactly countered by work being done by/on the system so there is no net temperature change.

Constant volume:

If ΔV = 0, then there can be no work done, (w=0), so q = ΔU.

Constant pressure:

This is the most common condition for chemical reactions, as the external pressure (ie, the atmosphere) remains constant for anything done in an open container, (like, say, a beaker). At constant pressure, ΔH = q.