Solving the P-V Diagram Ratio of p2/p1

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SUMMARY

The discussion focuses on calculating the ratio p2/p1 in a p-V diagram involving two paths for a gas transitioning from state a to state b. Path 1 requires 3.0p1V1 of energy as heat, while Path 2 requires 8.5p1V1. The solution derived from the energy balance equation ΔE=Q-W indicates that the ratio p2/p1 equals 8.5/3, confirming the relationship between pressure and energy transfer in thermodynamic processes.

PREREQUISITES
  • Understanding of thermodynamic principles, specifically the first law of thermodynamics.
  • Familiarity with p-V diagrams and their significance in thermodynamics.
  • Knowledge of energy transfer concepts, including heat (Q) and work (W).
  • Ability to manipulate algebraic equations to solve for variables.
NEXT STEPS
  • Study the first law of thermodynamics in detail, focusing on energy conservation.
  • Learn about different types of thermodynamic processes represented in p-V diagrams.
  • Explore the implications of heat transfer in various thermodynamic cycles.
  • Investigate the significance of area under the curve in p-V diagrams for work done calculations.
USEFUL FOR

Students studying thermodynamics, educators teaching gas laws, and professionals involved in energy systems analysis will benefit from this discussion.

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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
 
Last edited:
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There is no pV diagram that we can see.
 

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