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

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 $\frac{pounds}{in^{2}}$

          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 = $P_{1}V_{1} ln (\frac{V_{2}}{V_{1}})$

Putting the values into the above formula as follows.

                W = $P_{1}V_{1} ln (\frac{V_{2}}{V_{1}})$    

                     = $50 pounds/in^{2} \times 100 in^{3} \times ln (\frac{10}{100})$

                     = -11512.925 lbf-in

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

                W = $\frac{-11512.925}{12} lbf-ft$

                     = -959.41 lbf-ft

The negative sign means work is supplied.

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