Example 3:

Mass of piston: 1.57Kg

P_{initial} = 4.05 bar

T_{initial} = 305 K

Friction = 0

The process is quick, so: Q = 0

How high will the piston go??

A For an ideal gas:

B Ideal gas Low:

(constant moles)

Rearrange A:

Substitute for dT in B:

Combining terms:

Rearrange a couple of times:

Finally, integrate from in initial to top of tube:

For air:

What about the maximum height?

Using C:

Rearrange and use C+Pa:

Integrate:

Evaluate for v:

Once the piston leaves, it is in free fall!