### Isothermal vs. Non-Isothermal

Posted:

**Tue Feb 12, 2019 10:56 pm**Just for clarification, why do isothermal systems use the constant R and why don't non-isothermal systems use R?

Created by Dr. Laurence Lavelle

https://lavelle.chem.ucla.edu/forum/

https://lavelle.chem.ucla.edu/forum/viewtopic.php?f=128&t=42136

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Posted: **Tue Feb 12, 2019 10:56 pm**

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

Posted: **Tue Feb 12, 2019 11:16 pm**

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.