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1) The Ideal Gas Law, PV = RT, relates the pressure (P, in pascals), temperature (T, in Kelvin), and volume (V, in cubic meters) of 1 mole of a gas (with R = 8.314 as the universal gas constant), and describes the behavior of gases that do not liquefy easily, such as oxygen and hydrogen. We can solve the ideal gas law for volume and hence treat the volume as a function of the pressure and J mol K temperature: V(P,T) = 8.314T P a) Explain in detail what the trace of V with P = 1000 tells us about a key relationship between two quantities. b) Explain in detail what the trace of V with T = 5 tells us. c) Explain in detail what the level curve V = 0.5 tells us. d) Use 2 or 3 additional traces in each direction to make a rough sketch of the surface over the domain of V where P and T are non-negative. Write at least one sentence that describes the way the surface looks. e) Based on all your work above, write a couple of sentences that describe the effect that temperature and pressure have on volume.

1) The Ideal Gas Law, PV = RT, relates the pressure (P, in pascals), temperature (T, in Kelvin), and volume (V, in cubic meters) of 1 mole of a gas (with R = 8.314 as the universal gas constant), and describes the behavior of gases that do not liquefy easily, such as oxygen and hydrogen. We can solve the ideal gas law for volume and hence treat the volume as a function of the pressure and J mol K temperature: V(P,T) = 8.314T P a) Explain in detail what the trace of V with P = 1000 tells us about a key relationship between two quantities. b) Explain in detail what the trace of V with T = 5 tells us. c) Explain in detail what the level curve V = 0.5 tells us. d) Use 2 or 3 additional traces in each direction to make a rough sketch of the surface over the domain of V where P and T are non-negative. Write at least one sentence that describes the way the surface looks. e) Based on all your work above, write a couple of sentences that describe the effect that temperature and pressure have on volume.

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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mol K 1) The Ideal Gas Law, PV = RT, relates the pressure (P, in pascals), temperature (T, in Kelvin), and volume (V, in cubic meters) of 1 mole of a gas (with R = 8.314 as the universal gas constant), and describes the behavior of gases that do not liquefy easily, such as oxygen and hydrogen. We can solve the ideal gas law for volume and hence treat the volume as a function of the pressure and temperature: V(P,T) = 8.314T P 1000 tells us about a key relationship between a) Explain in detail what the trace of V with P two quantities. b) Explain in detail what the trace of V with T = 5 tells us. c) Explain in detail what the level curve V = 0.5 tells us. d) Use 2 or 3 additional traces in each direction to make a rough sketch of the surface over the domain of V where P and T are non-negative. Write at least one sentence that describes the way the surface looks. e) Based on all your work above, write a couple of sentences that describe the effect that temperature and pressure have on volume.
Transcribed Image Text:mol K 1) The Ideal Gas Law, PV = RT, relates the pressure (P, in pascals), temperature (T, in Kelvin), and volume (V, in cubic meters) of 1 mole of a gas (with R = 8.314 as the universal gas constant), and describes the behavior of gases that do not liquefy easily, such as oxygen and hydrogen. We can solve the ideal gas law for volume and hence treat the volume as a function of the pressure and temperature: V(P,T) = 8.314T P 1000 tells us about a key relationship between a) Explain in detail what the trace of V with P two quantities. b) Explain in detail what the trace of V with T = 5 tells us. c) Explain in detail what the level curve V = 0.5 tells us. d) Use 2 or 3 additional traces in each direction to make a rough sketch of the surface over the domain of V where P and T are non-negative. Write at least one sentence that describes the way the surface looks. e) Based on all your work above, write a couple of sentences that describe the effect that temperature and pressure have on volume.
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