Thermodynamics question – seems really easy? Help ASAP please?
The PV diagram for an ideal gas is shown in the figure above (I have included a description of the points on the graph below).
P1 = 4 atm, V1 = 1 liter, T1 = 200K
P2 = 1 atm, V2 = 4 liters, T2 = 800K
What is the net work done by the gas in the cyclic process from point A to point B to point C to point A?
Point A = P1, V1, T1
Point B = P1, V2, T2
Point C = P2, V2, T1
I thought A to B was constant pressure, so I used W = P(delta V).
B to C is constant volume, so W = 0.
C to A is constant temperature, so I used W = nRT ln (Vf/Vi).
The answer is +654 J, and I’m not getting that. I’m thinking I have to find the moles (n) of the gas somehow (I was just assuming it was 1 mol), but I have no idea how to do that! Thank you!!
Point A to Point B: W = (4 atm)(3 L) = 12 L*atm
Point B to Point C: W = 0 L*atm
Point C to Point A: W = nRT ln (Vf/Vi)
To use this equation, you need to find the number of moles using the equation PV=nRT for either P1 or P2 (they should work out to the same thing):
(4 atm)(1 L) = n(0.0821 L*atm/mol*K)(200 K)
n=0.2436 moles
W = nRT ln (Vf/Vi) = (0.2436 moles)(0.0821 L*atm/mol*K)(200 K)ln(1/4) = -5.545 L*atm
12 L*atm – 5.545 L*atm = 6.45 L*atm
6.45 L * atm = 654 J