Final answer:
The student's question involves calculating the work done by steam in a piston-cylinder device in physics, with two methods based on pressure-volume work and force-distance relationship.
Step-by-step explanation:
The question relates to the work done on a steam piston in a piston-cylinder device which is part of mechanical engineering, a subject within the field of physics. When steam at a given pressure is introduced into a piston-cylinder, it causes the piston to move. The work done by the expanding steam can be calculated using two different methods, both of which should provide the same result if the assumptions are correct.
To calculate the work done (part a), we use the formula W = PΔV, where 'P' is the pressure and 'ΔV' is the change in volume. Since the pressure is given as a gauge pressure, we do not need to correct for atmospheric pressure. The change in volume can be determined from the movement of the piston and its cross-sectional area. Once we have P and ΔV, we can find the work done by the steam.
For part (b), the work can alternatively be calculated by multiplying the force exerted by the piston (found from the pressure and the piston's cross-sectional area) by the distance the piston travels.
The question assumes a perfect piston-cylinder device without friction or heat losses, which resembles the conditions of an idealized physics problem. The key concepts involved here include pressure-volume (PV) work, gauge pressure, and mechanical work. In practice, the repeated expansion and contraction cycles in piston devices are used in engines and pumps, such as those found in old-fashioned steam locomotives or hand-driven tire pumps.