Question

A vapor is compressed in a frictionless piston-cylinder such that the volume changes from 100 to 10 in3 . The initial pressure is 50 psia and temperature is held constant at 100°F. Calculate the work in ft lbf. The vapor can be assumed to be an ideal gas.

Answer 1

Step-by-step explanation:

The given data is as follows.

Initial volume (
`V_(1)`) = 100
`in^(3)`

Final volume (
`V_(2)`) = 10
`in^(3)`

Initial pressure (
`P_(1)`) = 50 psia = 50
`(pounds)/(in^(2))`

Temperature =
`100^(o)F`

So, we assume that vapors are also ideal gas.

Hence, the work done for ideal gas will be calculated as follows.

W =
`P \int dV`

Since, it is given that the temperature is constant so, it is an isothermal process.

Therefore, work done for isothermal process is as follows.

W =
`P_(1)V_(1) ln ((V_(2))/(V_(1)))`

Putting the values into the above formula as follows.

W =
`P_(1)V_(1) ln ((V_(2))/(V_(1)))`

=
`50 pounds/in^(2) * 100 in^(3) * ln ((10)/(100))`

= -11512.925 lbf-in

As there are 12 inch present in 1 ft. So, converting lbf-in into lbf-ft as follows.

W =
`(-11512.925)/(12) lbf-ft`

= -959.41 lbf-ft

The negative sign means work is supplied.

Thus, we can conclude that the work done is -959.41 lbf-ft.