Question

I don't even know where to start with partials...

Evaluating a derivative of the van der Waals equation using the cyclic rule Find the partial derivatives (partial differential P/partial differential T)_V and (partial differential P/partial differential V)_T, and apply them to the equation derived from the cyclic rule, (partial differential V/partial differential T)_p = -(partial differential P/partial differential T)_V/(partial differential P/partial differential V)_T to find (partial differential_V/partial differential T)_P. Express your answer in terms of the parameters, and variables in the van der waals equation (p, V_m, R, T, a, and b) Applications to the van der waals equation of state For the van der Waals equation of state (V_m - b) (P + a/v^2_m) = RT where V_M is the molar volume, which is the volume divided by the moles of gas, n the derivative (partial differential V/* partial differential T)_P is difficult to obtain directly because finding an equation for V_m in terms of T or P requires solving the cubic equation PV^3_m - (bP + RT) V^2_m + a(V_m - b) = 0 where a and b are two parameters that take into account the size of the molecule and the attractive interaction. Because P is linear in the van der Waals equation, it should be easier to find the partial derivatives (partial differential P)/(partial differential Y)_V and (partial differential V/partial differential P)_T = 1/(partial differential P/partial differential V)_T needed to utilize the cyclic rule. Keep in mind that the cyclic rule for the variables V_m, P, and T is (partial differential V/partial differential T)_P (partial differential T/partial differential P)_V (partial differential P/partial differential V)_T = -1 For example, the partial derivation ((partial differential V/partial differential T)_P can be found by evaluating (partial differential V/partial differential T)_P = - (partial differential p/partial differential T)_V/(partial differential P/partial differential V)_T
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Answer 1

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