Chemistry Online

I am taking physical chemistry and we are using partial derivatives, I have never solved partials and need?

a little help.The problem reads: p=RT/V + (a+bT)/V^2 a and b are constants. Find (dV/dT) holding p constant. dV/dT is a partial derivative. It is a physical chemistry problem where we are looking at volume with respect to temperature while holding pressure constant. I attempted to isolate v, however I could not. Explanation would be helpful because I need to understand the process so I can repeat it in the future. Thanks in advance.

Public Comments

1. take d /dT of teh enitre equation, remember p is held constant 0 = R/V - RT/V^2 dV/dT +b/V^2 - 2(a+bT)/V^3 dV/dT Multiply by V^3 0 = RV^2 - RTV dV/dT +bV - 2(a+bT) dV/dT 0 = RV^2 + bV - (RTV + 2*[a+bT]) dV/dT dV/dT = {RV^2 + bV}/(RTV + 2*[a+bT])
2. To find a partial derivative, for example, with respect to T, consider all other variables to be held constant. You do not need to isolate V. So the partial of V is 0 = RN + b/V^2 + -2(a + bT)(dV/dT)/V^3. Now you can solve for dV/dT.
3. It is like derivatizing by using every term as a variable (except for the constants which have a derivative of 0, and p which is held constant). So you get : dp = 0 = RdT/V - (1/2)RTdV/V^2 + bdT/V^2 - (1/3)(a+bT)dV/V^3 by dividing by dT you get R/V - ((1/2)RT/V^2)dV/dT - b/V^2 -((1/3)(a+bT)/V^3)dV/dT = Rassemble all the term and you will find dV/dT expressed as a differential equation.