The Second Law of Thermodynamics
In this notes sheet...
The second law is used for a number of important calculations: finding temperature differences, reversibility, and efficiency of reversible vs irreversible heat engines.
Reversible & Irreversible Processes
Let us take the classic example of a quasi-equilibrium expansion:
If the mass on the piston is made up of a vast number of minuscule weights, like sand, removing a single grain pushes the piston up ever so slightly. The change is so small, that the return to equilibrium is almost instant.
For each grain of sand removed, we have an additional point on the P-V diagram – as pressure decreases, volume increases.
This process is reversible
It is reversible, because if we return the grains of sand one at a time, the piston will move down by the same amount. We neglect friction or leakage.
If, however, the weight consist of one large mass, and this is removed, the process is not in quasi-equilibrium.
The process is irreversible
In this example, the expansion itself is quasi-equilibrium, as we have returned to the grains of sand. However, when the piston hits the top or bottom stoppers, it makes a sound, releasing energy. This energy cannot be gotten back, so
The process is irreversible
What makes a process irreversible?
Friction
Unresisted expansion
Heat transfer to surroundings
Combustion
Mixing of different fluids
Clearly, then, the majority of real-life processes are irreversible.
The Second Law
Take the example of a spindle rotating in a container:
Spindle rotates
Gas in container heats up
Heat from gas is conducted through container and heats up the surroundings
If we reverse this:
Surroundings are heated
Gas inside container heats up
Spindle does not start rotating
We know from experience that this is the case, but why?
This is where the second law comes in:
Heat cannot be transferred from a cold body to a hotter body without a work input.
This is the all-important idea of direction: some things are allowed backwards as well as forwards, but many things are only allowed forwards.
Heat Engines & Efficiency
A heat engine is a device that connects a hot and cold reservoir with a work input or output.
From the first law:
The second law is often also used to describe efficiency, η:
Using the equation from the first law above, the efficiency can also be written as:
