Why is Work Negative in PV diagram?

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SUMMARY

The discussion clarifies the concept of work in a pressure-volume (PV) diagram, specifically addressing why work can be negative during an isothermal process. It establishes that work is calculated using the integral ∫P.dV, where a leftward movement along the volume (V) axis indicates negative dV. The net work for a cycle is determined by the areas under the curve in the PV diagram, with the area from points a to c representing work done by the system and the area from c to b representing work done on the system. If the direction of the cycle is reversed, the net work becomes positive.

PREREQUISITES
  • Understanding of pressure-volume (PV) diagrams
  • Familiarity with thermodynamic processes, particularly isothermal processes
  • Knowledge of integral calculus, specifically the concept of definite integrals
  • Basic principles of work and energy in thermodynamics
NEXT STEPS
  • Study the concept of work in thermodynamics using the equation W = ∫P.dV
  • Explore the implications of different thermodynamic cycles on work output
  • Learn about the significance of the area under the curve in PV diagrams
  • Investigate how reversing the direction of a thermodynamic cycle affects work calculations
USEFUL FOR

Students of thermodynamics, physics educators, and anyone seeking to understand the principles of work in pressure-volume diagrams.

lc99
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Homework Statement


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Homework Equations

The Attempt at a Solution


Was wonder how the isotherm is negative? Is it because it is going counterclockwise (the arrows)? If this is the case, i don't see why a-c would be positive work...

I'm just confused on whether work should be positive or negative... :(
 

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lc99 said:
Was wonder how the isotherm is negative? Is it because it is going counterclockwise (the arrows)? If this is the case, i don't see why a-c would be positive work...
It is not to do with the direction around the loop but rather the direction along the V axis. Work is ∫P.dV. If it is going leftward along the V axis then dV is negative.
This is taken care of by the integrals if you are careful with the limits.
 
From a→c, you are taking work out, from c→b, you are putting work in and since you are putting more work in that you are taking out, the net work is negative. You might think of it as one process at a time, the area under a→c represents the work out and the area under c→b represents the work in, the net work/cycle is the area enclosed on the p-V diagram. Of course if you reverse the direction around the enclosed area, the net work is positive.
 

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