Question

A cylinder with a moving piston expands from an initial volume of 0.250 L against an external pressure of 3.00 atm . The expansion does 235 J of work on the surroundings. What is the final volume of the cylinder?

Answer 1

1.02 L W = -P(V2 - V1) where W = Work P = Pressure V1 = Starting volume V2 = Ending volume Since the gas performed the work, the work needs to be negatively signed, so W = -235J. Since we have mixed units of atm and joules, we need to convert the pressure from atm to something more convenient. We can use a couple of the varients of the universal gas constant with different units. I'll use R = 8.314472 J/(mol*K) and R = 0.082057 L*atm/(mol*K), dividing the second by the first. So 0.082057 L*atm/(mol*K) / 8.314472 J/(mol*K) = 0.009869178 L*atm/J will be our conversion factor. Now for the math V2 = -W/P + V1 V2 = -(-235J * 0.009869178 L*atm/J) / 3.00 atm + 0.250 L V2 = -(-2.319256713 L*atm) / 3.00 atm + 0.250 L V2 = -(-0.773085571 L) + 0.250 L V2 = 0.773085571 L + 0.250 L V2 = 1.023085571 L Rounding to 3 significant figures gives 1.02 L