A thermodynamic cycle is a series of processes that cycle back to the same original state. These are very useful for modeling the operation of mechanical systems, such as the repeated motion of an internal combustion engine, or the movement of refrigeration fluid thorough each component in a refrigerator.
The conservation of energy governs every process in a thermodynamic cycle.
$$ Q-W=\Delta U_k+\Delta U_g+\Delta U_i=\frac 12m\Delta(v^2)+m\Delta z+m\Delta u $$
Since the cycle repeats the the exact same state, the first and last states are identical. As such, the changes to energy within the system across all the processes must cancel out to reach the original state. As such, the changes in kinetic, gravitational, and internal potential energies must sum to zero across the whole cycle.
$$ \Sigma\Delta U_k=\Sigma\Delta U_g=\Sigma\Delta U_i=0 $$
It is often helpful to represent the cycle in tabular form governed by the above equations. The conservation of energy governs each row. The prohibition of change to energy within the system governs the potential energy columns. More often than not, you will only be concerned with the overall internal energy, and so won’t need to consider each of the three types individually
| Process | $Q$ | $W$ | $\Delta U$ |
|---|---|---|---|
| 1-2 | |||
| 2-3 | |||
| 3-1 |
If the sum of work done by the system across all processes in a cycle is positive, then it is a power cycle, work is being done with energy received by heat transfer. As such, the cycle is practically useful for power generation.
If the work is negative, then heating of a cold body and cooling of a hot body is being achieved. As such, the cycle is practically useful for heating or cooling, and from different perspectives it is a heat pump cycle and a refrigeration cycle.
Consider a system which interacts with a hot reservoir and cold reservoir (A thermal reservoir is a body that does not appreciably change temperatures relative to the heat transfers it is experiencing, such as the ocean or earth). Across the whole cycle, the work done by the system is balanced with the heat transfer to these heat reservoirs.
$$ W_{sys}=Q_H-Q_C $$
We use efficiency coefficients to evaluate the performance of a particular power, heat, or cooling cycle. We will learn later in this course how the ideal performance may be determined.