Ideal Gas Law Change Rate Problem

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SUMMARY

The Ideal Gas Law, represented by the equation PV = nRT, is applied to determine the rate of change of temperature (dT/dt) for an ideal gas under specific conditions. Given that pressure (P) is 9.0 atm and increasing at 0.15 atm/min, while volume (V) is 13 L and decreasing at 0.16 L/min, the correct formula for dT/dt is derived as dT/dt = (PV' + VP') / nR. Substituting the values into the equation yields a result of 4.1291 K/min, which was not accepted by Web Assign, indicating a potential error in the interpretation of the rates of change.

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  • Understanding of the Ideal Gas Law (PV = nRT)
  • Knowledge of derivatives and rates of change in calculus
  • Familiarity with the concept of moles in chemistry
  • Basic proficiency in using Web Assign for homework problems
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  • Review the application of the chain rule in calculus for related rates problems
  • Study the implications of increasing and decreasing variables in the Ideal Gas Law
  • Practice additional problems involving the Ideal Gas Law and derivatives
  • Explore the use of Web Assign for troubleshooting common submission errors
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Students studying chemistry or physics, particularly those tackling problems related to the Ideal Gas Law and its applications in real-world scenarios.

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
 

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