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.

Explanation:

The given data is as follows.

    n = 2,          ,      

    = 300 K ,         = 500 K

     P = 1 bar

Equation for work done will be as follows.

                          W =

                              =

                              = - 3000 J

Hence, formula for heat added is as follows.

                       Q =

Putting given values into the above formula as follows.

                    Q =

                       =

                       = 11639.6 J

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

when the volume of gas is   changed from   717.73 ml   to 852 ml   the temperature will   change   from 315   c to 452   c

    calculation

this is calculated using the charles law formula

that is,   v1/t1 = v2/t2

          v1=?

        t1 = 315 c   into   kelvin = 315 +273 = 588 k

        v2 = 852   ml

        t2 = 425c + 273 =698 k

make v1   the subject of the formula ( by   multiplying both side by t1)

  v1=( v2 xt1) / t2

v1= (852 ml   x 588 k)/ 698 k= 717.73 ml