Ideal Gas Law Change Rate Problem

Kurani
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Homework Statement


The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 9.0 atm and is increasing at a rate of 0.15 atm/min and V = 13 L and is decreasing at a rate of 0.16 L/min. Find the rate of change of T with respect to time at that instant if n = 10 mol. (Round your answer to four decimal places.)


Homework Equations


PV=nRT
dT/dt = ___ K/min


The Attempt at a Solution


I was doing this problem on Web Assign and took the derivative of PV=nRT to get dT/dt=(PV'+VP')/nR and substituted in dT/dt=(9*.16+13*.15)/(10*.0821) and got 4.12911 but web assign doesn't accept it. I am not sure what I'm doing wrong. Thank you to anyone that can point me in the right direction.
 
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Hint: The volume V is decreasing.
 
lol, thanks a lot
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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