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5) In thermodynamics, the ideal gas law states that PV = NKT Here • N,k are constants • P is the pressure of the gas • V is the volume of the container • T is the temperature. Notice that you can play with this equation in several ways. For example: • You can think of P as a function of V and T NKT P V. So you can ӘР ӘР via the equation find the partial derivatives ᎧᎢ ' Ꮩ • You can think of T as a function of P and V T = via the equation ƏT the partial derivatives OP¹ av • You can think of V as a function of P and T V via the equation ᎧᏙ find the partial derivatives OP¹ ƏT a) What do you think ap ar av ar av ap = dy writes dt rule? PV Nk. So you can find ƏT NKT P. So you can Ꮩ . will be equal to, based on a "naive" manipulation of the symbols? Similar to how "naively" one dy dx dx dt in the case of the chain b) What do you actually find if you do the product of these partial derivatives? [hint: there is a video on our Canvas sites: Thermodynamics and Partial Derivatives, a Cautionary Tale, where I go over this.]

5) In thermodynamics, the ideal gas law states that PV = NKT Here • N,k are constants • P is the pressure of the gas • V is the volume of the container • T is the temperature. Notice that you can play with this equation in several ways. For example: • You can think of P as a function of V and T NKT P V. So you can ӘР ӘР via the equation find the partial derivatives ᎧᎢ ' Ꮩ • You can think of T as a function of P and V T = via the equation ƏT the partial derivatives OP¹ av • You can think of V as a function of P and T V via the equation ᎧᏙ find the partial derivatives OP¹ ƏT a) What do you think ap ar av ar av ap = dy writes dt rule? PV Nk. So you can find ƏT NKT P. So you can Ꮩ . will be equal to, based on a "naive" manipulation of the symbols? Similar to how "naively" one dy dx dx dt in the case of the chain b) What do you actually find if you do the product of these partial derivatives? [hint: there is a video on our Canvas sites: Thermodynamics and Partial Derivatives, a Cautionary Tale, where I go over this.]

Chemistry: Principles and Practice
Chemistry: Principles and Practice
3rd Edition
ISBN:9780534420123
Author:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Publisher:Daniel L. Reger, Scott R. Goode, David W. Ball, Edward Mercer
Chapter17: Chemcial Thermodynamics
Section: Chapter Questions
Problem 17.103QE: A 220-ft3 sample of gas at standard temperature and pressure is compressed into a cylinder, where it...
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Please assist me with homework question 5. Thanks in advance
5) In thermodynamics, the ideal gas law states that PV = NKT Here ● N,k are constants • P is the pressure of the gas • V is the volume of the container • T is the temperature. Notice that you can play with this equation in several ways. For example: • You can think of P as a function of V and T NKT P = via the equation V . So you can OP OP find the partial derivatives T av • You can think of T as a function of P and V PV T via the equation Nk. So you can find ƏT ƏT the partial derivatives OP' av • You can think of V as a function of P and T NkT V = via the equation P . So you can ᎧᏙ av find the partial derivatives Op' ar a) What do you think ᎧᏢ ᏭᎢ ᏭᏙ ƏT Əv ƏP will be equal to, based on a "naive" manipulation of the symbols? Similar to how "naively" one dy dy dx dx dt in the case of the chain writes dt rule? b) What do you actually find if you do the product of these partial derivatives? [hint: there is a video on our Canvas sites: Thermodynamics and Partial Derivatives, a Cautionary Tale, where I go over this.]
Transcribed Image Text:5) In thermodynamics, the ideal gas law states that PV = NKT Here ● N,k are constants • P is the pressure of the gas • V is the volume of the container • T is the temperature. Notice that you can play with this equation in several ways. For example: • You can think of P as a function of V and T NKT P = via the equation V . So you can OP OP find the partial derivatives T av • You can think of T as a function of P and V PV T via the equation Nk. So you can find ƏT ƏT the partial derivatives OP' av • You can think of V as a function of P and T NkT V = via the equation P . So you can ᎧᏙ av find the partial derivatives Op' ar a) What do you think ᎧᏢ ᏭᎢ ᏭᏙ ƏT Əv ƏP will be equal to, based on a "naive" manipulation of the symbols? Similar to how "naively" one dy dy dx dx dt in the case of the chain writes dt rule? b) What do you actually find if you do the product of these partial derivatives? [hint: there is a video on our Canvas sites: Thermodynamics and Partial Derivatives, a Cautionary Tale, where I go over this.]
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