# Isothermal Process for an Ideal Gas

## Ideal Gas EOS

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for an

on an

#### ideal gas

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because:
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### Ch 4, Lesson A, Page 18 - Isothermal Process for an Ideal Gas

• Now, let’s consider an isothermal process in which an ideal gases goes from state 1 to state 2.
• The ideal gas equation of state can be rearranged to give us our path equation, P as a function of V.
• N and R are constants, so they can be pulled out of the integral, but what about T ?
• In general, YOU CANNOT pull T out of the integral.
• So, the ideal gas EOS or any other EOS does not BY ITSELF define the process path.  We need one more piece of information.
• In this case, that extra piece of information is that the process follows an ISOTHERMAL path.
• Therefore, T is a constant and in this special case, T CAN be pulled outside of the integral.
• This yields an integral that is straightforward to solve.
• The result in the yellow box will allow us to calculate the boundary work that crosses the system boundary when an ideal gas expands or is compressed isothermally.
• Now, let’s take a look at a slightly more complicated process path.

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