Final answer:
The energy transfer by work during the expansion of propane in a piston-cylinder assembly where pv^2 is constant cannot be calculated accurately without additional data such as the specific volumes at the initial and final states.
Step-by-step explanation:
To find the energy transfer by work for a piston-cylinder assembly containing propane that undergoes expansion while maintaining the relationship pv2=constant, we need to integrate the work done from the initial to the final state. For processes where pressure-volume relationship is given by pvn=constant, the work done W is given by:
W = (p1v1 - p2v2)/(1 - n), where n is the polytropic index.
However, since in this problem the propane's pressure and specific volume relationship states pv2=constant, here n = 2. Hence, the equation simplifies to W = p1v1 - p2v2 because division by zero is not possible, indicating an isothermal process.
The work done for an isothermal process for an ideal gas can also be represented by W = nRT ln(v2/v1), but this equation is not directly applicable here due to the lack of information regarding the number of moles n, the universal gas constant R, and the temperatures.
To proceed, we would normally use the specific volume and mass of the gas to find the initial and final volumes and plug them into our first work equation. Unfortunately, the question lacks the values of specific volume needed to calculate the work done by the propane during expansion. Therefore, with the given data, it is not possible to calculate an exact value for the work done, and only an estimate or additional data would help in providing a precise answer.