Solving the P-V Diagram Ratio of p2/p1

[aub]

Homework Statement

The p-V diagram in the figure below shows two paths along which a sample of gas can be taken from state a to state b, where Vb = 4.0V1. Path 1 requires that energy equal to 3.0p1V1 be transferred to the gas as heat. Path 2 requires that energy equal to 8.5p1V1 be transferred to the gas as heat. What is the ratio p2/p1?

http://edugen.wiley.com/edugen/courses/crs1650/art/qb/qu/c18/pict_18_96.gif

Homework Equations

ΔE=change in internal energy=Q-W (=heat-work)

The Attempt at a Solution

I tried to work this way but it's wrong..

ΔE₂=ΔE₁
8.5p₁v₁ - 3v₁*(p₂-p₁)/2 (<--area inside the triangle)= 3p₁v₁
8.5p₁v₁ - 3p₂v₁ + 3p₁v₁ = 3p₁v₁
8.5p₁ = 3p₂
p₂/p₁=8.5/3

 

[kuruman]

There is no pV diagram that we can see.