Question

By heating 2 mol of nitrogen gas in a frictionless piston-cylinder, the gas expands at a constant pres- sure of 1 bar from an initial volume of 0.02 m² to a final volume of 0.05 m. The gas temperature correspondingly increases from 300 to 500 K. Assuming nitrogen is an ideal gas with a molar heat capacity CP = R (where R is the gas constant), find the amount of heat added and work derived from the gas expansion.

Answer 1

Explanation:

The given data is as follows.

    n = 2,          $V_{1} = 0.02 m^{2}$,       $V_{2} = 0.05 m^{2}$

   $T_{1} = 0.02 m^{2}$ = 300 K ,         $T_{2}$ = 500 K

     P = 1 bar

Equation for work done will be as follows.

                          W = $-P \times \Delta V$

                              = $-1 bar \times (0.05 m^{2} - 0.02 m^{2})$

                              = - 3000 J

Hence, formula for heat added is as follows.

                       Q = $nC_{p} \Delta T$

Putting given values into the above formula as follows.

                    Q = $nC_{p} \Delta T$

                       = $2 \times \frac{7}{2} \times (500 K - 300 K)$

                       = 11639.6 J

Thus, we can conclude that the amount of heat added is 11639.6 J.