A

To find the work done by the paddle wheel to raise the piston, we need to consider the work done against the atmospheric pressure when raising the piston. The work done (W) against a constant pressure can be calculated using the formula:

W = P_{ext} \cdot \Delta V
Where:
W = Work done (in lbf·in)
P_{ext} = External pressure (in lbf/in²)
\Delta V = Change in volume (in in³)

1. **Identify the parameters**:
- The force on the piston: 175 lbf
- The distance the piston is raised: 5 in

2. **Calculate the volume change** (since 1 in² = 1 in x 1 in):
\Delta V = A \cdot d, where A = area of the piston face, and d = displacement.
If we assume a standard piston area or are not given any area information, we can use direct pressure effects using force and distance:

3. **Calculate Work**:
Since the work done is directly related to the force and distance the piston moves. Thus, we can express:
W = F \cdot d
W = 175 \text{ lbf} \cdot 5 \text{ in} = 875 \text{ lbf·in}

Hence, the work required is 875 lbf·in and should be interpreted against the required units (if converting to other units is needed).
Given that we are looking for the amount of work input, the answer is that the total work to be input by the paddle wheel is 875 lbf·in.