IB Physics Sub-topic B4 Notes

Laws of thermodynamics

In Topic B.1 – B.3, you learned about the basics of thermal energy transfers and gas laws. For HL students, you are expected to know more detail, starting with the four laws of thermodynamics.

0. Zeroth law – if two systems are in thermodynamic equilibrium with a third system, then they are in thermodynamic equilibrium with one another. This is a roundabout way of saying that these two systems have the same temperature.
1. First law – as per the law of conservation of energy, a closed system exhibiting a change in energy converts this into other forms to maintain total energy. In other words, energy cannot be created nor destroyed, but only changes forms.
2. Second law – in a closed system, spontaneous processes are not spontaneously irreversible, and consequently increase the disorder (entropy) of the universe. 
3. Third law – when an isolated system reaches a temperature of absolute zero, its entropy reaches a constant value.

Within these laws, two terms need to be defined:

1. Closed system – a closed system does not allow mass to transfer in or out but allows energy to transfer in and out in the forms of heat or work.
2. Isolated system – an isolated system does not allow mass or energy to transfer in or out.

The Zeroth law was effectively covered in B.1, so does not need further evaluation. However, you are expected to know the first and second laws in depth, so let’s cover these one-by-one.

The first law of thermodynamics

The first law essentially rephrases the law of conservation of energy in the context of thermal energy transfer. Here, a few types of energy are at play:

1. Heat (Q) – the thermal energy transferred in or out of a system.
2. Internal energy (U) – the system’s energy as a sum of its particles’ kinetic energy and the potential energy between particles. Remember that for temperature-dependent changes in internal energy, the formulae are:

   $\Delta U = \frac{3}{2} N k_{b} \Delta T = \frac{3}{2} Rn \Delta T$

    
3. Thermodynamic work (W) – the energy exerted on a system by its surroundings (negative) or by a system on its surroundings (positive) that causes a macroscopic force to act on the system. The macroscopic force is quantified by change in volume of the system. Thus, if there is no volume change due to a resultant external force, there is no work being done. The formula for this is:

   $W = P \Delta V$

The three quantities above are invariably related to one another as the exertion of work by a system on its surroundings would decrease its internal energy, whereas heat supplied to the system increases its internal energy. The formula for this is:

$\Delta U = Q - W$

This equation can be adjusted algebraically to isolate any one of the other two variables. The IB prefers to label it as the heat transfer being equal to the change in internal energy and work exerted. The formula for this is:

$Q = \Delta U + W$