Find dP/dz and pressure and density as function of height for a slab of air 1-16
Автор: Marx Academy
Загружено: 2016-10-16
Просмотров: 19704
An Introduction to Thermal Physics
Daniel V. Schroeder
Problem 1-16
Consider a horizontal slab of air whose thickness (height) is dz. if this slab is at rest the pressure holding it up from below must balance both the pressure from above and the weight of the slab. Use this fact to find an expression for dP/dz, the variation of pressure with altitude in terms of the density of air
b) Use the ideal gas law to write the density of air in terms of pressure, temperature and the average mass m of the air molecules. ( Take air as 78% N2, 21% O2 and 1 % argon. Show then that the pressure obeys the differential equation dp/dz=-mgP/kT
c) Assuming that the temperature of the atmosphere is independent of height, solve the barometric equation to obtain the pressure as a function of height P(z)=P(0)e^-(mgz/kT). Show also that the density obeys a similar equation
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