Final answer:
The work done by the steam on a piston in a steam locomotive can be computed by calculating the pressure-volume work, yielding a result of approximately 176 kJ, which does not match the options provided. This suggests a potential issue with the original question options.
Step-by-step explanation:
The subject of this question is Physics, specifically relating to work done by a piston in a steam engine. To calculate the work done by the steam on the piston as it moves through a distance, we can use the formula for work done in a constant pressure process, which is W = pΔV, where W is the work, p is the pressure, and ΔV is the change in volume.
First, we need to find the change in volume (ΔV). We do this by calculating the volume of the cylinder changed when the piston moves the given distance. The formula for the volume of a cylinder is V = πr^2h, where r is the radius of the piston, and h is the height or the distance the piston moves. In this case, r = 0.200 m and h = 0.800 m.
ΔV = π(0.200 m)^2(0.800 m) = π(0.04 m^2)(0.800 m) = π(0.032 m^3).
Now we find the work done by the steam using the given pressure (p = 1.75×10^6 N/m^2):
W = pΔV = (1.75×10^6 N/m^2)(π×0.032 m^3).
Since π is approximately 3.14159, we can compute W ≈ (1.75×10^6 N/m^2)(3.14159×0.032 m^3) ≈ 1750000 × 0.1005304 m^3 ≈ 175883.52 J.
The work done by the steam is therefore approximately 176 kJ (kiljoules), which is not one of the options provided in the question. If we consider only the options given, it is possible that there might be a miscalculation or misunderstanding in the question itself. To verify the work done, we can also calculate the force exerted by the steam and multiply by the distance traveled. Since F = pA (where A is the cross-sectional area of the piston), and the work is W = Fd:
F = pA = (1.75×10^6 N/m^2)(π×(0.200 m)^2) = 1.75×10^6 N/m^2 × 0.1256 m^2 ≈ 219800 N.
Then, W = Fd = (219800 N)(0.800 m) = 175840 J ≈ 176 kJ, confirming our earlier result.