Question

A well-insulated, closed device claims to be able to compress 100 mol of propylene, acting as a SoaveRedlich-Kwong gas and with C ∗ P = 100 J/(mol·K), from 300 K and 2 m3 to 800 K and 0.02 m3 by using less than 5 MJ of work. Is this possible?

Answer 1

Explanation:

The given data is as follows.

    Moles of propylene = 100 moles,    $T_{i}$ = 300 K

    $T_{f}$ = 800 K,    $V_{i} = 2 m^{3}$

    $V_{f} = 0.02 m^{3}$,   $C_{p}$ of propylene = 100 J/mol

Now, we assume the following assumptions:

Since, it is a compression process therefore, work will be done on the system. And, work done will be equal to the heat energy liberating without any friction.

            W = $mC_{p} \Delta T$

     $100 moles \times 100 J/mol K (800 - 300) K$

                 = $5 \times 10^{6} J$

                 = 5 MJ

Thus, we can conclude that a minimum of 5 MJ work is required without any friction.