An ideal diatomic gas in a piston expands according to the g

An ideal diatomic gas in a piston expands according to the graph. Determine the work done by the gas in going from state A to state C.
(include units with answer)

Solution

Work done = Area under ABC line and volume axis

            W = Area under AB line and volume axis + Area under BC line and volume axis

Area under AB line and volume axis = Area of triangle between P1 andP2 + Area of rectangle under P1

                                                    =[(1/2)base xheight ] +[length x width]

                                                    =[0.5x(V2-V1)(P2-P1)]+[P1 x(V2-V1)]

                                                    = [0.5 x(9.8-6.4)(5.2 atm-1 atm)] +[1 atm (9.8-6.4)]

                                                 = [0.5 x3.4 x 4.2 x 1.01 x10 ⁵ ] +[(1.01x10 ⁵)(3.4) ] Since 1 atm = 1.01 x10 ⁵ Pa

                                                = 1.06454 x10 ⁶ J

Area under BC line and volume axis = P1 (V3-V2)

                                                    = 1 atm (16.1 - 9.8)

                                                   = 1.01 x10 ⁵ x6.3

                                                   = 0.6363x10 ⁶ J

Therefore W = (1.06454 x10 ⁶ J )+( 0.6363x10 ⁶ J)

                  = 1.70084 x10 ⁶ J