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Calculus/partial derivative

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Expert: - 9/9/2010


Question
Hi thanks for your help, I need to find a partial derivative of this function,
vanderwaals gas equation:

(p+(a*n^2/v^2))*(v-n*b)=n*r*t

find the partial dV/dN.  I can not solve for V though, i don't know how to do
this....I am confused how to do the implicit diff, and can not figure it out.  
Thanks alot!!

Answer
This reminds me of the equation pV = nrt, no?
Here, p, V, and r could all be functions of time with n as the number of moles.

Using that theory, we would get the following when p', V', and r' are the derivatives with respect to t.

This breaks down to fg = h where f = p + a*n*^2/V^2, g = v-n*b,
and h = n*r*t.

The derivative would be f'g + g'f = h'.

It can be said that f' = p' - (2*a*n^2/V^3)(V') , g' = v' (since n and b are constants, right?), and h'= nr.

Putting in the values of f', g, g', f, and h' will let V' be figured out.  This requires multiplying out the equation, keep terms with V; on the left, subtracting off terms on the left that have no V' from both sides, factoring V' out of the terms on the left, and dividing both sides of the equation by what was factored out on the left.

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