I am working on differentiating the ideal gas equation PV = nrT with respect to time.
In the question I have to solve n is a constant.
Specifically, trying to find the change in pressure: P = (nRT)/V
I am getting myself confused because when I initially tried to solve this problem I took n and R out of the equation to give P' = nR [T' / V'], and then differentiated it using the quotient rule.
However, I have since realized that keeping the constants in the equation and differentiating them both to 1 gives different result to taking them outside the derivative equation and multiplying by the non-differentiated n and R. I am unsure on what basis you would take them out of the original equation in the first place (although I have seen this done with mathematical differentiation???]
Any advice would great.
Well, differentiating the equation gives $\mathrm d (PV)=\mathrm d(kT),$ or $$P\mathrm dV+V\mathrm dP=k\mathrm dT.$$ Then we have that $$P\frac{\mathrm dV}{\mathrm dt}+V\frac{\mathrm dP}{\mathrm dt}=k\frac{\mathrm dT}{\mathrm dt}.$$