# Lesson Plan: Entropy and the Second and Third Laws of Thermodynamics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to calculate the entropy of systems and the entropy change of systems that transfer internal energy to each other.

#### Objectives

Students will be able to

- recall that the term
*entropy*is a quantity associated with the properties of systems that are qualitatively described in terms like*randomness*or*disorder*of the systems, - recognize that energy transfers between systems are associated with changes of the entropies of the systems,
- define an irreversible process as one in which either pressure, volume, or temperature change in a noncontinuous manner or energy is dissipated,
- recall that, for an irreversible energy transfer between systems, the net change of entropy of the systems must be greater than zero,
- define a reversible process as one in which the pressure, volume, or temperature of the system either remain constant or change continuously and in which no energy is dissipated,
- recall that, for a reversible energy transfer between systems, the net change of entropy of the systems is zero,
- recognize that the entropy increase of an ideal heat engine that does work can be modeled as being proportional to the decrease in the useful work that can be done per joule of internal energy transferred between the reservoirs of the heat engine due to the heating of its low temperature reservoir and the cooling of its high temperature reservoir,
- recognize that, in a reversible transfer of energy, the change in the entropy of a system due to the energy transfer to or from the system is given by the equation , where is the change in entropy of the system, is the heating of the system, and is the temperature of the system,
- apply the equation in all combinations,
- recognize that the entropy of a system of equivalent particles can be modeled as being proportional to the natural logarithm of the number of possible arrangements of the particles, where the possible arrangements are the states of the system,
- calculate the entropy of a system using the equation , where is the Boltzmann constant and is the number of states of the system,
- recognize that, as a heat pump decreases the temperature of its low-temperature reservoir, the work required per joule of cooling of the low temperature increases, and so a heat pump can never decrease the temperature of an object to zero kelvin.

#### Prerequisites

Students should already be familiar with

- the first law of thermodynamics,
- heat engines,
- heat pumps.

#### Exclusions

Students will not cover

- formal justification of the impossibility of using a heat pump to decrease the temperature of an object to zero kelvin.