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W=-Pext(deltaV) is used when there is a constant external pressure outside of a system, and the system irreversibly expands into its surroundings, doing a certain amount of work. W=-nRTlnv2/v1 is used for a much more nuanced system, in which the external pressure is not constant but is instead subject to very, very small fluctuations. Think of it as a piston inside a larger, sealed container. The reason this expansion is called "reversible" is that any change in the external pressure will be counteracted and "reversed": for example, a decrease in the pressure outside of the piston will cause the volume of the gas in the piston to expand, thereby increasing the pressure outside the piston and pushing the gas back down. All of this happens in very small increments. And it is isothermal, so it remains the same temperature the entire time. Hope this makes sense.
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