Hello, I'm a first year physics student and in thermodynamics we always use [tex] \frac{1}{ \frac{dX}{dY} } = \frac{dY}{dX} [/tex] and I was wondering 'how true' this is, i.e. what are the conditions for this to be true? For example, if I have the equation of state of a Vanderwaals gas: [tex]\left( P + \frac{an^2^}{V^2^}\right) \left(V + bn \right) = nRT[/tex] and I want to find [tex]\left( \frac{dV}{dT} \right)_P[/tex], can I just calculate [tex]\left( \frac{dT}{dV} \right)_P[/tex] (which is(adsbygoogle = window.adsbygoogle || []).push({}); mucheasier) and then take the reciproque?

(If not, is there another way?)

Thank you.

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# Taking the reciproque of a partial derivative (as seen in thermodynamics)?

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