510024 J of work are done on the gas in the process shown in

510.024 J of work are done on the gas in the process shown in the figure where the volume units are cubic meters. What is the final volume in cubic centimeters?

Solution

As shown in the graph, the work is done on the gas at constant pressure of P = 200 kPa

Also, the volume of the gas changes from 3Vf to Vf.

Now, we know that the work done on a gas is given as: W = PV

But the work done on the gas has already been provided, hence we will equate that with the above expression and the resolve to find the value for Vf

That is, PV = 200 x 10³ x (3Vf - Vf) = 510.024

or, 200 x 10³ x 2Vf = 510.024

or, Vf = 510.024 / 200 x 10³ x 2 = 1.27506 x 10^-3 m³

Therefore the required final volume is 1275.06 cm³