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For the equation W=-nRTlnV2/V1, if the temperature stays constant, why is it included in the equation but for the other work equation W=-PdeltaV if the temperature changes along the pathway, why is temperature not included in the equation?
in the second equation the pressure is constant and the volume is changing in response so everything on the other side of the ideal gas law equation stays constant, i'm not sure why we don't include it though.
I think temperature is not included in w=-pΔV, because it is a closed system and the pressure is constant, so when you change the temperature by adding or removing heat, the only thing that it affects is the volume. So the temperature change is manifested in the volume.
I think you have to include T in the first equation because when you derive it you have to use the integral of P in respect to volume, but you ultimately replace P with the other side of the ideal gas equation (nRT/V). When you take the integral, you can pull out the "-nRT" because it's technically a constant. You still have to include it because if it wasn't there you wouldn't be taking the integral of P in respect to volume, which is work.
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