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(Kittel 6.11) Convective isentropic equilibrium of the atmosphere. The lower 10- 15 km of the atmosphere - the troposphere -is often in a convective steady state at constant entropy, not constant temperature. In such equilibrium pV is independent of altitude, where y = C₁/C₁. Use the condition of mechanical equilibrium in a uniform gravitational field to: (a) Show that dT/dz = constant, where z is the altitude. This quantity, important in meteorology, is called the dry adiabatic lapse rate. (Do not use the barometric pressure relation that was derived in Chapter 5 for an isothermal atmosphere.) (b) Estimate dT/dz, in degrees Celsius per km. Take y = 7/5. (c) Show that p~ p', where p is the mass density. If the actual temperature gradient is greater than the isentropic gradient, the atmosphere may be unstable with respect to convection.

(Kittel 6.11) Convective isentropic equilibrium of the atmosphere. The lower 10- 15 km of the atmosphere - the troposphere -is often in a convective steady state at constant entropy, not constant temperature. In such equilibrium pV is independent of altitude, where y = C₁/C₁. Use the condition of mechanical equilibrium in a uniform gravitational field to: (a) Show that dT/dz = constant, where z is the altitude. This quantity, important in meteorology, is called the dry adiabatic lapse rate. (Do not use the barometric pressure relation that was derived in Chapter 5 for an isothermal atmosphere.) (b) Estimate dT/dz, in degrees Celsius per km. Take y = 7/5. (c) Show that p~ p', where p is the mass density. If the actual temperature gradient is greater than the isentropic gradient, the atmosphere may be unstable with respect to convection.

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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5. (Kittel 6.11) Convective isentropic equilibrium of the atmosphere. The lower 10- 15 km of the atmosphere - the troposphere -is often in a convective steady state at constant entropy, not constant temperature. In such equilibrium pV² is independent of altitude, where y = C₁/C. Use the condition of mechanical equilibrium in a uniform gravitational field to: (a) Show that dT/dz = constant, where z is the altitude. This quantity, important in meteorology, is called the dry adiabatic lapse rate. (Do not use the barometric pressure relation that was derived in Chapter 5 for an isothermal atmosphere.) (b) Estimate dT/dz, in degrees Celsius per km. Take y = 7/5. (c) Show that p- p², where p is the mass density. If the actual temperature gradient is greater than the isentropic gradient, the atmosphere may be unstable with respect to convection.
Transcribed Image Text:5. (Kittel 6.11) Convective isentropic equilibrium of the atmosphere. The lower 10- 15 km of the atmosphere - the troposphere -is often in a convective steady state at constant entropy, not constant temperature. In such equilibrium pV² is independent of altitude, where y = C₁/C. Use the condition of mechanical equilibrium in a uniform gravitational field to: (a) Show that dT/dz = constant, where z is the altitude. This quantity, important in meteorology, is called the dry adiabatic lapse rate. (Do not use the barometric pressure relation that was derived in Chapter 5 for an isothermal atmosphere.) (b) Estimate dT/dz, in degrees Celsius per km. Take y = 7/5. (c) Show that p- p², where p is the mass density. If the actual temperature gradient is greater than the isentropic gradient, the atmosphere may be unstable with respect to convection.
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