- Accounting
- Aerospace Engineering
- Anatomy
- Anthropology
- Arts & Humanities
- Astronomy
- Biology
- Business
- Chemistry
- Civil Engineering
- Computer Science
- Communications
- Economics
- Electrical Engineering
- English
- Finance
- Geography
- Geology
- Health Science
- History
- Industrial Engineering
- Information Systems
- Law
- Linguistics
- Management
- Marketing
- Material Science
- Mathematics
- Mechanical Engineering
- Medicine
- Nursing
- Philosophy
- Physics
- Political Science
- Psychology
- Religion
- Sociology
- Statistics

HomeStudy GuidesPhysics

Menu

The Nature of Science and Physics

Kinematics

Introduction to One-Dimensional KinematicsDisplacementVectors, Scalars, and Coordinate SystemsTime, Velocity, and SpeedVideo: One-Dimensional KinematicsAccelerationMotion Equations for Constant Acceleration in One DimensionProblem-Solving Basics for One-Dimensional KinematicsFalling ObjectsGraphical Analysis of One-Dimensional Motion

Two-Dimensional Kinematics

Dynamics: Force and Newton's Laws of Motion

Introduction to Dynamics: Newton's Laws of MotionDevelopment of Force ConceptNewton's First Law of Motion: InertiaNewton's Second Law of Motion: Concept of a SystemNewton's Third Law of Motion: Symmetry in ForcesVideo: Newton's LawsNormal, Tension, and Other Examples of ForcesProblem-Solving StrategiesFurther Applications of Newton's Laws of MotionExtended Topic: The Four Basic Forces—An Introduction

Further Applications of Newton's Laws: Friction, Drag, and Elasticity

Uniform Circular Motion and Gravitation

Introduction to Uniform Circular Motion and GravitationRotation Angle and Angular VelocityCentripetal AccelerationCentripetal ForceFictitious Forces and Non-inertial Frames: The Coriolis ForceNewton's Universal Law of GravitationVideo: GravitationSatellites and Kepler's Laws: An Argument for Simplicity

Work, Energy, and Energy Resources

Introduction to Work, Energy, and Energy ResourcesWork: The Scientific DefinitionKinetic Energy and the Work-Energy TheoremGravitational Potential EnergyVideo: Potential and Kinetic EnergyConservative Forces and Potential EnergyNonconservative ForcesConservation of EnergyPowerWork, Energy, and Power in HumansWorld Energy Use

Linear Momentum and Collisions

Rotational Motion and Angular Momentum

Introduction to Rotational Motion and Angular MomentumAngular AccelerationKinematics of Rotational MotionVideo: Rotational MotionDynamics of Rotational Motion: Rotational InertiaRotational Kinetic Energy: Work and Energy RevisitedAngular Momentum and Its ConservationVideo: Angular MomentumCollisions of Extended Bodies in Two DimensionsGyroscopic Effects: Vector Aspects of Angular Momentum

Statics and Torque

Fluid Statics

Introduction to Fluid StaticsWhat Is a Fluid?DensityPressureVariation of Pressure with Depth in a FluidPascal's PrincipleGauge Pressure, Absolute Pressure, and Pressure MeasurementArchimedes' PrincipleVideo: BuoyancyCohesion and Adhesion in Liquids: Surface Tension and Capillary ActionPressures in the Body

Fluid Dynamics and Its Biological and Medical Applications

Introduction to Fluid Dynamics and Biological and Medical ApplicationsFlow Rate and Its Relation to VelocityBernoulli's EquationVideo: Fluid FlowThe Most General Applications of Bernoulli's EquationViscosity and Laminar Flow; Poiseuille's LawThe Onset of TurbulenceMotion of an Object in a Viscous FluidMolecular Transport Phenomena: Diffusion, Osmosis, and Related Processes

Temperature, Kinetic Theory, and the Gas Laws

Heat and Heat Transfer Methods

Thermodynamics

Introduction to ThermodynamicsThe First Law of ThermodynamicsThe First Law of Thermodynamics and Some Simple ProcessesIntroduction to the Second Law of Thermodynamics: Heat Engines and Their EfficiencyCarnot's Perfect Heat Engine: The Second Law of Thermodynamics RestatedApplications of Thermodynamics: Heat Pumps and RefrigeratorsEntropy and the Second Law of Thermodynamics: Disorder and the Unavailability of EnergyStatistical Interpretation of Entropy and the Second Law of Thermodynamics: The Underlying Explanation

Oscillatory Motion and Waves

Introduction to Oscillatory Motion and WavesHooke's Law: Stress and Strain RevisitedPeriod and Frequency in OscillationsSimple Harmonic Motion: A Special Periodic MotionVideo: Harmonic MotionThe Simple PendulumEnergy and the Simple Harmonic OscillatorUniform Circular Motion and Simple Harmonic MotionDamped Harmonic MotionForced Oscillations and ResonanceWavesSuperposition and InterferenceEnergy in Waves: Intensity

Physics of Hearing

- Explain the relationship between vapor pressure of water and the capacity of air to hold water vapor.
- Explain the relationship between relative humidity and partial pressure of water vapor in the air.
- Calculate vapor density using vapor pressure.
- Calculate humidity and dew point.

The expression “it’s not the heat, it’s the humidity” makes a valid point. We keep cool in hot weather by evaporating sweat from our skin and water from our breathing passages. Because evaporation is inhibited by high humidity, we feel hotter at a given temperature when the humidity is high. Low humidity, on the other hand, can cause discomfort from excessive drying of mucous membranes and can lead to an increased risk of respiratory infections.

When we say humidity, we really mean

The capacity of air to hold water vapor is based on vapor pressure of water. The liquid and solid phases are continuously giving off vapor because some of the molecules have high enough speeds to enter the gas phase; see Figure 2a. If a lid is placed over the container, as in Figure 2b, evaporation continues, increasing the pressure, until sufficient vapor has built up for condensation to balance evaporation. Then equilibrium has been achieved, and the vapor pressure is equal to the partial pressure of water in the container. Vapor pressure increases with temperature because molecular speeds are higher as temperature increases. Table 1 gives representative values of water vapor pressure over a range of temperatures.

Relative humidity is related to the partial pressure of water vapor in the air. At 100% humidity, the partial pressure is equal to the vapor pressure, and no more water can enter the vapor phase. If the partial pressure is less than the vapor pressure, then evaporation will take place, as humidity is less than 100%. If the partial pressure is greater than the vapor pressure, condensation takes place. The capacity of air to “hold” water vapor is determined by the vapor pressure of water and has nothing to do with the properties of air.

Table 1. Saturation Vapor Density of Water | ||
---|---|---|

Temperature (ºC) | Vapor pressure (Pa) | Saturation vapor density (g/m^{3}) |

−50 | 4.0 | 0.039 |

−20 | 1.04 × 10^{2 } |
0.89 |

−10 | 2.60 × 10^{2 } |
2.36 |

0 | 6.10 × 10^{2 } |
4.84 |

5 | 8.68 × 10^{2 } |
6.80 |

10 | 1.19 × 10^{3 } |
9.40 |

15 | 1.69 × 10^{3 } |
12.8 |

20 | 2.33 × 10^{3 } |
17.2 |

25 | 3.17 × 10^{3 } |
23.0 |

30 | 4.24 × 10^{3 } |
30.4 |

37 | 6.31 × 10^{3 } |
44.0 |

40 | 7.34 × 10^{3 } |
51.1 |

50 | 1.23 × 10^{4 } |
82.4 |

60 | 1.99 × 10^{4 } |
130 |

70 | 3.12 × 10^{4 } |
197 |

80 | 4.73 × 10^{4 } |
294 |

90 | 7.01 × 10^{4 } |
418 |

95 | 8.59 × 10^{4 } |
505 |

100 |
1.01 × 10^{5} |
598 |

120 | 1.99 × 10^{5 } |
1095 |

150 | 4.76 × 10^{5 } |
2430 |

200 | 1.55 × 10^{6 } |
7090 |

220 | 2.32 × 10^{6 } |
10,200 |

temperature *T *= 20ºC = 293 K

vapor pressure *P* of water at 20ºC is 2.33 × 10^{3} Pa

molecular mass of water is 18.0 g/mol

2. Solve the ideal gas law for$\frac{n}{V}\\$

: $\frac{n}{V}=\frac{P}{RT}\\$

3. Substitute known values into the equation and solve for $\displaystyle\frac{n}{V}=\frac{P}{RT}=\frac{2.33\times10^3\text{ Pa}}{(8.31\text{ J/mol}\cdot\text{ K})(293\text{ K})}=0.957\text{ mol/m}^3\\$

4. Convert the density in moles per cubic meter to grams per cubic meter.$\displaystyle\rho=\left(0.957\frac{\text{mol}}{\text{m}^3}\right)\left(\frac{18.0\text{ g}}{\text{mol}}\right)=17.2\text{ g/m}^3\\$

$\displaystyle\text{percent relative humidity}=\frac{\text{vapor density}}{\text{saturation vapor density}}\times100\\$

2. At what temperature will this air reach 100% relative humidity (the saturation density)? This temperature is the dew point.

3. What is the humidity when the air temperature is 25.0ºC and the dew point is –10.0ºC?

$\displaystyle\text{percent relative humidity}=\frac{\text{vapor density}}{\text{saturation vapor density}}\times100\\$

2. The first is given to be 9.40 g/m$\displaystyle\text{percent relative humidity}=\frac{9.40\text{ g/m}^3}{23.0\text{ g/m}^3}\times100=40.9\%\\$

3. The air contains 9.40 g/mHere, the dew point temperature is given to be –10.0ºC. Using Table 1, we see that the vapor density is 2.36 g/m

$\displaystyle\text{percent relative humidity}=\frac{2.36\text{ g/m}^3}{23.0\text{ g/m}^3}\times100=10.3\%\\$

- Relative humidity is the fraction of water vapor in a gas compared to the saturation value.
- The saturation vapor density can be determined from the vapor pressure for a given temperature.
- Percent relative humidity is defined to be $\text{percent relative humidity}=\frac{\text{vapor density}}{\text{saturation vapor density}}\times100\\$.
- The dew point is the temperature at which air reaches 100% relative humidity.

- Because humidity depends only on water’s vapor pressure and temperature, are the saturation vapor densities listed in Table 1 valid in an atmosphere of helium at a pressure of 1.01 × 10
^{5}N/m^{2}, rather than air? Are those values affected by altitude on Earth? - Why does a beaker of 40.0ºC water placed in a vacuum chamber start to boil as the chamber is evacuated (air is pumped out of the chamber)? At what pressure does the boiling begin? Would food cook any faster in such a beaker?
- Why does rubbing alcohol evaporate much more rapidly than water at STP (standard temperature and pressure)?

- Dry air is 78.1% nitrogen. What is the partial pressure of nitrogen when the atmospheric pressure is 1.01 × 10
^{5}N/m^{2}? - (a) What is the vapor pressure of water at 20.0ºC? (b) What percentage of atmospheric pressure does this correspond to? (c) What percent of 20.0ºC air is water vapor if it has 100% relative humidity? (The density of dry air at 20.0ºC is 1.20kg/m3.)
- Pressure cookers increase cooking speed by raising the boiling temperature of water above its value at atmospheric pressure. (a) What pressure is necessary to raise the boiling point to 120.0ºC? (b) What gauge pressure does this correspond to?
- (a) At what temperature does water boil at an altitude of 1500 m (about 5000 ft) on a day when atmospheric pressure is 8.59 × 10
^{4}N/m^{2}? (b) What about at an altitude of 3000 m (about 10,000 ft) when atmospheric pressure is 7.00 × 10^{4}N/m^{2}? - What is the atmospheric pressure on top of Mt. Everest on a day when water boils there at a temperature of 70.0ºC?
- At a spot in the high Andes, water boils at 80.0ºC, greatly reducing the cooking speed of potatoes, for example. What is atmospheric pressure at this location?
- What is the relative humidity on a 25.0ºC day when the air contains 18.0 g/m
^{3}of water vapor? - What is the density of water vapor in g/m
^{3}on a hot dry day in the desert when the temperature is 40.0ºC and the relative humidity is 6.00%? - A deep-sea diver should breathe a gas mixture that has the same oxygen partial pressure as at sea level, where dry air contains 20.9% oxygen and has a total pressure of 1.01 × 10
^{5}N/m^{2}. (a) What is the partial pressure of oxygen at sea level? (b) If the diver breathes a gas mixture at a pressure of 2.00 × 10^{6}N/m^{2}, what percent oxygen should it be to have the same oxygen partial pressure as at sea level? - The vapor pressure of water at 40.0ºC is 7.34 × 10
^{3}N/m^{2}. Using the ideal gas law, calculate the density of water vapor in g/m^{3}that creates a partial pressure equal to this vapor pressure. The result should be the same as the saturation vapor density at that temperature 51.1 g/m^{3}. - Air in human lungs has a temperature of 37.0ºC and a saturation vapor density of 44.0 g/m
^{3}. (a) If 2.00 L of air is exhaled and very dry air inhaled, what is the maximum loss of water vapor by the person? (b) Calculate the partial pressure of water vapor having this density, and compare it with the vapor pressure of 6.31 × 10^{3}N/m^{2}. - If the relative humidity is 90.0% on a muggy summer morning when the temperature is 20.0ºC, what will it be later in the day when the temperature is 30.0ºC, assuming the water vapor density remains constant?
- Late on an autumn day, the relative humidity is 45.0% and the temperature is 20.0ºC. What will the relative humidity be that evening when the temperature has dropped to 10.0ºC, assuming constant water vapor density?
- Atmospheric pressure atop Mt. Everest is 3.30 × 10
^{4}N/m^{2}. (a) What is the partial pressure of oxygen there if it is 20.9% of the air? (b) What percent oxygen should a mountain climber breathe so that its partial pressure is the same as at sea level, where atmospheric pressure is 1.01 × 10^{5}N/m^{2}? (c) One of the most severe problems for those climbing very high mountains is the extreme drying of breathing passages. Why does this drying occur? - What is the dew point (the temperature at which 100% relative humidity would occur) on a day when relative humidity is 39.0% at a temperature of 20.0ºC?
- On a certain day, the temperature is 25.0ºC and the relative humidity is 90.0%. How many grams of water must condense out of each cubic meter of air if the temperature falls to 15.0ºC? Such a drop in temperature can, thus, produce heavy dew or fog.
**Integrated Concepts.**The boiling point of water increases with depth because pressure increases with depth. At what depth will fresh water have a boiling point of 150ºC, if the surface of the water is at sea level?**Integrated Concepts.**(a) At what depth in fresh water is the critical pressure of water reached, given that the surface is at sea level? (b) At what temperature will this water boil? (c) Is a significantly higher temperature needed to boil water at a greater depth?**Integrated Concepts.**To get an idea of the small effect that temperature has on Archimedes’ principle, calculate the fraction of a copper block’s weight that is supported by the buoyant force in 0ºC water and compare this fraction with the fraction supported in 95.ºC water.**Integrated Concepts.**If you want to cook in water at 150ºC, you need a pressure cooker that can withstand the necessary pressure. (a) What pressure is required for the boiling point of water to be this high? (b) If the lid of the pressure cooker is a disk 25.0 cm in diameter, what force must it be able to withstand at this pressure?**Unreasonable Results.**(a) How many moles per cubic meter of an ideal gas are there at a pressure of 1.00 × 10^{14}N/m^{2}and at 0ºC? (b) What is unreasonable about this result? (c) Which premise or assumption is responsible?**Unreasonable Results.**(a) An automobile mechanic claims that an aluminum rod fits loosely into its hole on an aluminum engine block because the engine is hot and the rod is cold. If the hole is 10.0% bigger in diameter than the 22.0ºC rod, at what temperature will the rod be the same size as the hole? (b) What is unreasonable about this temperature? (c) Which premise is responsible?**Unreasonable Results.**The temperature inside a supernova explosion is said to be 2.00 × 10^{13}K. (a) What would the average velocity*v*_{rms}of hydrogen atoms be? (b) What is unreasonable about this velocity? (c) Which premise or assumption is responsible?**Unreasonable Results.**Suppose the relative humidity is 80% on a day when the temperature is 30.0ºC. (a) What will the relative humidity be if the air cools to 25.0ºC and the vapor density remains constant? (b) What is unreasonable about this result? (c) Which premise is responsible?

3. (a) 1.99 × 10

5. 3.12 × 10

7. 78.3%

9. (a) 2.12 × 10

11. (a) 8.80 × 10

13. 82.3%

15. 4.77ºC

17. 38.3 m

19.

$\displaystyle\frac{\frac{F_{\text{B}}}{w_{\text{Cu}}}}{\frac{F_{\text{B}}}{w_{\text{Cu}}{\prime}}}=1.02\\$

. The buoyant force supports nearly the exact same amount of force on the copper block in both circumstances.21. (a) 4.41 × 10

23. (a) 7.03 × 10