# 3.5 Humidity, evaporation, and boiling  (Page 3/9)

 Page 3 / 9

## Percent relative humidity

We define percent relative humidity    as the ratio of vapor density to saturation vapor density, or

$\text{percent relative humidity}=\frac{\text{vapor density}}{\text{saturation vapor density}}×\text{100}$

We can use this and the data in [link] to do a variety of interesting calculations, keeping in mind that relative humidity is based on the comparison of the partial pressure of water vapor in air and ice.

## Calculating humidity and dew point

(a) Calculate the percent relative humidity on a day when the temperature is $\text{25}\text{.}0\text{º}\text{C}$ and the air contains 9.40 g of water vapor per ${\text{m}}^{3}$ . (b) At what temperature will this air reach 100% relative humidity (the saturation density)? This temperature is the dew point. (c) What is the humidity when the air temperature is $\text{25}\text{.}0\text{º}\text{C}$ and the dew point is $–\text{10}\text{.}0\text{º}\text{C}$ ?

Strategy and Solution

(a) Percent relative humidity is defined as the ratio of vapor density to saturation vapor density.

$\text{percent relative humidity}=\frac{\text{vapor density}}{\text{saturation vapor density}}×\text{100}$

The first is given to be $9\text{.}{\text{40 g/m}}^{3}$ , and the second is found in [link] to be $\text{23}\text{.}{\text{0 g/m}}^{3}$ . Thus,

$\text{percent relative humidity}=\frac{9\text{.}{\text{40 g/m}}^{3}}{\text{23}\text{.}{\text{0 g/m}}^{3}}×\text{100}=\text{40}\text{.}9\text{}\text{.%}$

(b) The air contains $9\text{.}{\text{40 g/m}}^{3}$ of water vapor. The relative humidity will be 100% at a temperature where $9\text{.}{\text{40 g/m}}^{3}$ is the saturation density. Inspection of [link] reveals this to be the case at $\text{10}\text{.}0\text{º}\text{C}$ , where the relative humidity will be 100%. That temperature is called the dew point for air with this concentration of water vapor.

(c) Here, the dew point temperature is given to be $–\text{10}\text{.}0\text{º}\text{C}$ . Using [link] , we see that the vapor density is $2\text{.}{\text{36 g/m}}^{3}$ , because this value is the saturation vapor density at $–\text{10}\text{.}0\text{º}\text{C}$ . The saturation vapor density at $\text{25}\text{.}0\text{º}\text{C}$ is seen to be $\text{23}\text{.}{\text{0 g/m}}^{3}$ . Thus, the relative humidity at $\text{25}\text{.}0\text{º}\text{C}$ is

$\text{percent relative humidity}=\frac{2\text{.}{\text{36 g/m}}^{3}}{\text{23}\text{.}{\text{0 g/m}}^{3}}×\text{100}=\text{10}\text{.}3\text{%}\text{}\text{.}$

Discussion

The importance of dew point is that air temperature cannot drop below $\text{10}\text{.}0\text{º}\text{C}$ in part (b), or $–\text{10}\text{.}0\text{º}\text{C}$ in part (c), without water vapor condensing out of the air. If condensation occurs, considerable transfer of heat occurs (discussed in Heat and Heat Transfer Methods ), which prevents the temperature from further dropping. When dew points are below $0\text{ºC}$ , freezing temperatures are a greater possibility, which explains why farmers keep track of the dew point. Low humidity in deserts means low dew-point temperatures. Thus condensation is unlikely. If the temperature drops, vapor does not condense in liquid drops. Because no heat is released into the air, the air temperature drops more rapidly compared to air with higher humidity. Likewise, at high temperatures, liquid droplets do not evaporate, so that no heat is removed from the gas to the liquid phase. This explains the large range of temperature in arid regions.

Why does water boil at $\text{100}\text{º}\text{C}$ ? You will note from [link] that the vapor pressure of water at $\text{100}\text{º}\text{C}$ is $1\text{.}\text{01}×{\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}\text{Pa}$ , or 1.00 atm. Thus, it can evaporate without limit at this temperature and pressure. But why does it form bubbles when it boils? This is because water ordinarily contains significant amounts of dissolved air and other impurities, which are observed as small bubbles of air in a glass of water. If a bubble starts out at the bottom of the container at $\text{20}\text{º}\text{C}$ , it contains water vapor (about 2.30%). The pressure inside the bubble is fixed at 1.00 atm (we ignore the slight pressure exerted by the water around it). As the temperature rises, the amount of air in the bubble stays the same, but the water vapor increases; the bubble expands to keep the pressure at 1.00 atm. At $\text{100}\text{º}\text{C}$ , water vapor enters the bubble continuously since the partial pressure of water is equal to 1.00 atm in equilibrium. It cannot reach this pressure, however, since the bubble also contains air and total pressure is 1.00 atm. The bubble grows in size and thereby increases the buoyant force. The bubble breaks away and rises rapidly to the surface—we call this boiling! (See [link] .)

#### Questions & Answers

where we get a research paper on Nano chemistry....?
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!