×
Log in to StudySoup
Get Full Access to An Introduction To Thermal Physics - 1 Edition - Chapter 5 - Problem 36p
Join StudySoup for FREE
Get Full Access to An Introduction To Thermal Physics - 1 Edition - Chapter 5 - Problem 36p

Already have an account? Login here
×
Reset your password

Effect of altitude on boiling water.(a) Use the result of

An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder ISBN: 9780201380279 40

Solution for problem 36P Chapter 5

An Introduction to Thermal Physics | 1st Edition

  • Textbook Solutions
  • 2901 Step-by-step solutions solved by professors and subject experts
  • Get 24/7 help from StudySoup virtual teaching assistants
An Introduction to Thermal Physics | 1st Edition | ISBN: 9780201380279 | Authors: Daniel V. Schroeder

An Introduction to Thermal Physics | 1st Edition

4 5 1 303 Reviews
22
3
Problem 36P

Effect of altitude on boiling water.

(a) Use the result of the previous problem 1 and the data in below Figure to plot a graph of the vapor pressure of water between 50°C and 100°C. How well can you match the data at the two endpoints?

(b) Reading the graph backwards, estimate the boiling temperature of water at each of the locations for which you determined the pressure in Problem 2. Explain why it takes longer to cook noodles when you’re camping in the mountains.

(c) Show that the dependence of boiling temperature on altitude is very nearly (though not exactly) a linear function, and calculate the slope in degrees Celsius per thousand feet (or in degrees Celsius per kilometer).

Figure: Phase diagram for H2O (not to scale). The table gives the vaporpressure and molar latent heat for the solid-gas transformation (first three entries)and the liquid-gas transformation (remaining entries). Data from Keenan et al.(1978) and Lide (1994).

Problem 1:

The Clausius-Clapeyron below relation is a differential equation that can, in principle, be solved to find the shape of the entire phase-boundary curve. To solve it, however, you have to know how both L and ΔV depend on temperature and pressure. Often, over a reasonably small section of the curve, you can take L to be constant. Moreover, if one of the phases is a gas, you can usually neglect the volume of the condensed phase and just take ΔV to be the volume of the gas, expressed in terms of temperature and pressure using the ideal gas law. Making all these assumptions, solve the differential equation explicitly to obtain the following formula for the phase boundary curve:

P = (constant) × e–L/RT,

This result is called the vapour pressure equation. Caution: Be sure to use this formula only when all the assumptions just listed are valid.

Relation:

Problem 2:

The exponential atmosphere.

(a) 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. (The information needed to calculate m is given in Problem.) Show, then, that the pressure obeys the differential equation

called the barometric equation.

(c) Assuming that the temperature of the atmosphere is independent of height (not a great assumption but not terrible either), 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.

(d) Estimate the pressure, in atmospheres, at the following locations: Ogden, Utah (4700 ft or 1430 m above sea level); Leadville, Colorado (10,150 ft, 3090 m) ; Mt. Whitney, California (14,500 ft, 4420 m); Mt. Everest, Nepal/Tibet (29,000 ft, 8850 m). (Assume that the pressure at sea level is 1 atm.)

Problem 3:

Calculate the mass of a mole of dry air, which is a mixture of N2 (78% by volume), O2 (21%), and argon (1%).

Step-by-Step Solution:
Step 1 of 3

Nature of Earth’s Atmosphere Earth’s three atmospheres -composition of today’s atmosphere Surface processes and earth-atm. Gas exchanges Density and Pressure Layers of the Atmosphere -temp patterns vertically -nature of troposphere and stratosphere -environmental lapse rate (ELR) Special Features: water vapor and clouds Dust (scatters light, etc.) Jet streams (transports hear etc) Ozone layer -Magnetosphere earth ‘s three atmosphere: Origional atmosphere unknown composition Second atmosphere mainly water vapor and CO2 (from volcanic outgassing) Third atmosphere oxygen righ 20% (after photosynthesis developed)

Step 2 of 3

Chapter 5, Problem 36P is Solved
Step 3 of 3

Textbook: An Introduction to Thermal Physics
Edition: 1
Author: Daniel V. Schroeder
ISBN: 9780201380279

This full solution covers the following key subjects: pressure, equation, temperature, gas, air. This expansive textbook survival guide covers 10 chapters, and 454 solutions. The full step-by-step solution to problem: 36P from chapter: 5 was answered by , our top Physics solution expert on 07/05/17, 04:29AM. This textbook survival guide was created for the textbook: An Introduction to Thermal Physics , edition: 1. The answer to “Effect of altitude on boiling water.(a) Use the result of the previous problem 1 and the data in below Figure to plot a graph of the vapor pressure of water between 50°C and 100°C. How well can you match the data at the two endpoints?________________(b) Reading the graph backwards, estimate the boiling temperature of water at each of the locations for which you determined the pressure in 2. Explain why it takes longer to cook noodles when you’re camping in the mountains.________________(c) Show that the dependence of boiling temperature on altitude is very nearly (though not exactly) a linear function, and calculate the slope in degrees Celsius per thousand feet (or in degrees Celsius per kilometer).Figure: Phase diagram for H2O (not to scale). The table gives the vaporpressure and molar latent heat for the solid-gas transformation (first three entries)and the liquid-gas transformation (remaining entries). Data from Keenan et al.(1978) and Lide (1994). 1:The Clausius-Clapeyron below relation is a differential equation that can, in principle, be solved to find the shape of the entire phase-boundary curve. To solve it, however, you have to know how both L and ?V depend on temperature and pressure. Often, over a reasonably small section of the curve, you can take L to be constant. Moreover, if one of the phases is a gas, you can usually neglect the volume of the condensed phase and just take ?V to be the volume of the gas, expressed in terms of temperature and pressure using the ideal gas law. Making all these assumptions, solve the differential equation explicitly to obtain the following formula for the phase boundary curve:P = (constant) × e–L/RT,This result is called the vapour pressure equation. Caution: Be sure to use this formula only when all the assumptions just listed are valid.Relation: 2:The exponential atmosphere.(a) 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. (The information needed to calculate m is given in Problem.) Show, then, that the pressure obeys the differential equation called the barometric equation.________________(c) Assuming that the temperature of the atmosphere is independent of height (not a great assumption but not terrible either), 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.________________(d) Estimate the pressure, in atmospheres, at the following locations: Ogden, Utah (4700 ft or 1430 m above sea level); Leadville, Colorado (10,150 ft, 3090 m) ; Mt. Whitney, California (14,500 ft, 4420 m); Mt. Everest, Nepal/Tibet (29,000 ft, 8850 m). (Assume that the pressure at sea level is 1 atm.) 3:Calculate the mass of a mole of dry air, which is a mixture of N2 (78% by volume), O2 (21%), and argon (1%).” is broken down into a number of easy to follow steps, and 524 words. An Introduction to Thermal Physics was written by and is associated to the ISBN: 9780201380279. Since the solution to 36P from 5 chapter was answered, more than 286 students have viewed the full step-by-step answer.

Other solutions

People also purchased

Related chapters

Unlock Textbook Solution

Enter your email below to unlock your verified solution to:

Effect of altitude on boiling water.(a) Use the result of