Final Answer:
The work done (w41) on the gas as it is heated from state 4 to state 1 can be expressed as w41 = p0 * (v1 - v4), where p0 is the initial pressure, v1 is the final volume, and v4 is the initial volume.
Step-by-step explanation:
In the formula w41 = p0 * (v1 - v4), p0 represents the initial pressure of the gas, v1 is the final volume, and v4 is the initial volume. To calculate the work done during the process, we subtract the initial volume from the final volume and then multiply it by the initial pressure. This formula is derived from the definition of work done in a thermodynamic system, where work (w) is equal to the force applied (pressure, p) multiplied by the distance over which the force is applied (change in volume, v).
In this context, the subscript 1 denotes the final state, and the subscript 4 denotes the initial state. Therefore, (v1 - v4) represents the change in volume during the heating process. By multiplying this change in volume by the initial pressure (p0), we obtain the work done on the gas as it undergoes the specified transformation.
It's essential to express the answer in terms of p0 and v0 as these variables represent the initial conditions of the gas. This allows for a more general and applicable representation of the work done, considering the specific initial state of the gas as it transitions from state 4 to state 1.