The negative sign of external pressure in Work Equation

$w=-P\Delta V$
and
$w=-\int_{V_{1}}^{V_{2}}PdV=-nRTln\frac{V_{2}}{V_{1}}$

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The negative sign of external pressure in Work Equation

Hi Professor Lavelle!
Is the external pressure negative since the action being done goes against the external pressure?

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Re: The negative sign of external pressure in Work Equation

The negative sign in front of the equation relates the fact that work done by the system on the surroundings is "negative work" and work done by the surroundings on the system is "positive work". The sign will switch from negative to positive if $V_{2}$ > $V_{1}$ (the system is shrinking in volume because work is being done on it). Thus the pressure is not what becomes negative, but the initial and final volumes effect the sign.

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