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If you have an initial estimate for the pressure, $p_0$, then you can quickly solve iteritively for the pressure that matches the desired entropy $s=s^*$ using modified Newton's method: $$p_{n+1}=p_n-\frac{s(p_n,T)-s*}{\left(\frac{\partial s}{\partial p}\right)_T}$$The partial derivative of s with respect to p can be obtained by finite difference at the ...

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