A particular gas is enclosed in a cylinder with a moveable piston. It is observed that if the walls are adiabatic, a quasi-static increase in volume results in a decrease in pressure according to the equation
a ) Find the quasi-static work done on the system and the net heat transfer to the system in each of the three processes (ADB, ACB, and the direct linear process AB ) as shown in the figure.
In the process ADB the gas is heated at constant pressure ( P = 10^5 Pa) until its volume increases from its initial value of 10^-3 m^3 to its final value of 8e-3 m^3. The gas is then cooled at constant volume until its pressure decreases to 10^5/32 Pa. The other processes (ACB and AB) can be similarly interpreted, according to the figure.
P^3*V^5 =Constant for Q=0
I am currently only having trouble with the part with the direct linear process AB.
dQ = δU - δW
W = -PdV
The Attempt at a Solution
When it says it is directly linear, I took that to mean the following:
P*V = Px*Vx
Where Px and Vx are the initial pressure and volume. From there I integrated the work equation and got the following:
W = -Px*Vx*ln(Vb/Va).
I then did the same thing with the P^3*V^5 = Constant equation, but when I used these, as worked with the previous parts. My answers did not match the ones given in the book (W = - 360.9 J and Q = 248.4J)
I appreciate any help, thanks!