## Isothermal vs. Non-Isothermal

isochoric/isometric: $\Delta V = 0$
isothermal: $\Delta T = 0$
isobaric: $\Delta P = 0$

sallina_yehdego 2E
Posts: 75
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### Isothermal vs. Non-Isothermal

Just for clarification, why do isothermal systems use the constant R and why don't non-isothermal systems use R?

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Joined: Fri Sep 28, 2018 12:22 am
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### Re: Isothermal vs. Non-Isothermal

When the system is not isothermal, the equations like work are w= -PdeltaV. When the isothermal factor is added, when the delta v is a series of infintesimal changes so you can integrate: so the equation becomes w= - integral from V1 to V2 of P dv. P can then be replaced with nRT/V from the ideal gas law. Then when we pull out the constant and take the integral, we get the equation w= -nRT ln(V2/V1). The R comes from the replacement of P when we are taking the integral that is why the isothermal ones have it.