Thermodynamics Need help for AP test in 40 minutes

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SUMMARY

The discussion focuses on calculating work done during an isothermal expansion of a gas, specifically using the integral of pressure with respect to volume. The work done by the gas is represented as the integral \(\int P \, dv\), where a positive change in volume (dv) results in a positive area under the pressure-volume (PV) graph. The participants confirm that the work done by the gas is indeed the positive area under the curve, while the work done on the gas is the negative of this value.

PREREQUISITES
  • Understanding of isothermal processes in thermodynamics
  • Familiarity with pressure-volume (PV) diagrams
  • Knowledge of integral calculus
  • Basic concepts of work in thermodynamics
NEXT STEPS
  • Study the First Law of Thermodynamics and its applications
  • Learn about different types of thermodynamic processes, including isothermal and adiabatic
  • Explore the derivation of work done in isothermal expansions using calculus
  • Review examples of PV diagrams and the significance of area under the curve
USEFUL FOR

Students preparing for AP Physics exams, educators teaching thermodynamics, and anyone interested in understanding the principles of work in gas systems.

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Thermodynamics! Need help for AP test in 40 minutes!

Lets say that you have a gas that starts at an initial pressure P, volume V, and temperate T.

Then it undergoes an isothermal expansion, during with pressure decreases and volume increases.

What is the work done BY the gas during the transition?
What is the work done ON the gas during the transition?

Now, if I want to do this with integrals (i.e. area under the curve), for work done BY the gas, would it be the POSITIVE AREA under the curve?
 
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about 20 minutes now...anyone?
 


ƒ(x) said:
Lets say that you have a gas that starts at an initial pressure P, volume V, and temperate T.

Then it undergoes an isothermal expansion, during with pressure decreases and volume increases.

What is the work done BY the gas during the transition?
What is the work done ON the gas during the transition?

Now, if I want to do this with integrals (i.e. area under the curve), for work done BY the gas, would it be the POSITIVE AREA under the curve?
Yes. Work done by the gas is \int Pdv. If dv is positive, the integral (area under PV graph) is positive.

AM
 

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