Question

Steam to drive an old-fashioned steam locomotive is supplied at a constant gauge pressure of 1.75×106N/m2 (about 250 psi) to a piston with a 0.200-m radius. (a) By calculating PΔV, find the work done by the steam when the piston moves 0.800 m. Note that this is the net work output, since gauge pressure is used. (b) Now find the amount of work by calculating the force exerted times the distance traveled. Is the answer the same as in part (a)?

a) 224 kJ, No
b) 448 kJ, Yes
c) 672 kJ, No
d) 896 kJ, Yes

Answer 1

The work done by the steam when the piston moves 0.800 m is 224 kJ. The amount of work calculated by force exerted times distance traveled is 448 kJ, which is different from the answer in part (a).

Step-by-step explanation:

In order to find the work done by the steam when the piston moves 0.800 m, we can use the formula:

Work = Pressure x Change in Volume

Since the piston moves linearly, we can use the formula:

Change in Volume = π x (Final Radius^2 - Initial Radius^2) x Distance

Using the given values, the work done comes out to be 224 kJ.

For part (b), we can calculate the force exerted by the steam on the piston using the formula:

Force = Pressure x Area

Then, we can find the work done by multiplying the force by the distance traveled. The answer for this part is 448 kJ. So, the answer is not the same as in part (a). Therefore, the correct answer is (c) 672 kJ, No.