I will be checking for organization, conceptual understanding, and proper mathem

Question

I will be checking for organization, conceptual understanding, and proper mathematical communication, as well as completion of the problems. 10 out of 50 total points are for organizational and use of the proper mathematical communication (Please read "SUGGESTIONS FOR GRADED PROBLEMS WRITE-UP AND MATHEMATICS IN GENERAL ") Show as much work as you can, draw sketches if necessary and clearly explain why you are doing what you are doing. Use correct mathematical notation. You may work with your classmates. However, please submit your own work! Please use this sheet as a cover page. The Ideal Gas Law The ideal gas law states that if n moles of gas has volume V and temperature T and is under pressure P, then the following relationship holds: PV = nRT, where R is the universal gas constant. The ideal gas law allows us to express each of P, V, or T as a function of the other two. Show that partial differential V/partial differential T partial differential T/partial differential P partial differential P/partial differential V = -1

Explanation / Answer

PV= nRT

V= nRT/P

(dV/dT)P= nR/P

T= PV/nR

(dT/dP)V= V/nR

P= nRT/V

(dP/dV)T= -nRT/V2, (dV/dT)P* (dT/dP)V* (dP/dV)T= -(nR/P)* (V/nR) (nRT/V2) = -n2R2VT/ (PnRV2)= -nRT/PV= -1

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