<< Chapter < Page Chapter >> Page >

Percent relative humidity

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

percent relative humidity = vapor density saturation vapor density × 100 size 12{ size 11{"percent relative humidity"= { { size 11{"vapor density"}} over { size 11{"saturation vapor density"}} } times "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 25 . 0 º C size 12{"25" "." 0°C} {} and the air contains 9.40 g of water vapor per m 3 size 12{m rSup { size 8{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 25 . 0 º C size 12{"25" "." 0°C} {} and the dew point is 10 . 0 º C size 12{ +- "10" "." 0°C} {} ?

Strategy and Solution

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

percent relative humidity = vapor density saturation vapor density × 100 size 12{ size 11{"percent relative humidity"= { { size 11{"vapor density"}} over { size 11{"saturation vapor density"}} } times "100"}} {}

The first is given to be 9 . 40 g/m 3 size 12{9 "." "40 g/m" rSup { size 8{3} } } {} , and the second is found in [link] to be 23 . 0 g/m 3 size 12{"23" "." "0 g/m" rSup { size 8{3} } } {} . Thus,

percent relative humidity = 9 . 40 g/m 3 23 . 0 g/m 3 × 100 = 40 . 9 .% size 12{ size 11{"percent relative humidity"= { { size 11{9 "." "40 g/m" rSup { size 8{3} } }} over { size 12{"23" "." "0 g/m" rSup { size 8{3} } } } } ´"100"="40" "." 9% "." }} {}

(b) The air contains 9 . 40 g/m 3 size 12{9 "." "40 g/m" rSup { size 8{3} } } {} of water vapor. The relative humidity will be 100% at a temperature where 9 . 40 g/m 3 size 12{9 "." "40 g/m" rSup { size 8{3} } } {} is the saturation density. Inspection of [link] reveals this to be the case at 10 . 0 º C size 12{"10" "." 0°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 10 . 0 º C size 12{ +- "10" "." 0°C} {} . Using [link] , we see that the vapor density is 2 . 36 g/m 3 size 12{2 "." "36 g/m" rSup { size 8{3} } } {} , because this value is the saturation vapor density at 10 . 0 º C size 12{ +- "10" "." 0°C} {} . The saturation vapor density at 25 . 0 º C size 12{"25" "." 0°C} {} is seen to be 23 . 0 g/m 3 size 12{"23" "." "0 g/m" rSup { size 8{3} } } {} . Thus, the relative humidity at 25 . 0 º C size 12{"25" "." 0°C} {} is

percent relative humidity = 2 . 36 g/m 3 23 . 0 g/m 3 × 100 = 10 . 3 % . size 12{ size 11{"percent relative humidity"= { { size 11{2 "." "36 g/m" rSup { size 8{3} } }} over { size 12{"23" "." "0 g/m" rSup { size 8{3} } } } } ×"100"="10" "." 3% "." }} {}

Discussion

The importance of dew point is that air temperature cannot drop below 10 . 0 º C size 12{"10" "." 0°C} {} in part (b), or 10 . 0 º C size 12{ +- "10" "." 0°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 ºC size 12{0°C} {} , 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 100 º C size 12{"100"°C} {} ? You will note from [link] that the vapor pressure of water at 100 º C size 12{"100"°C} {} is 1 . 01 × 10 5 Pa size 12{1 "." "01"´"10" rSup { size 8{5} } " 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 20 º C size 12{"20"°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 100 º C size 12{"100"°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

what is torque
Deepak Reply
The turning effect of force is called torque.
Uzair
what there factors affect the surface tension of a liquid
Promise Reply
formula for impedance
muyiwa Reply
ehat is central forces
Nita Reply
what is distance?
Jonathan Reply
What does mean ohms law imply
Victoria Reply
ohms law state that the electricity passing through a metallic conductor is directly proportional to the potential difference across its end
muyiwa
what is matter
folajin Reply
Anything that occupies space
Kevin
Any thing that has weight and occupies space
Victoria
Anything which we can feel by any of our 5 sense organs
Suraj
Right
Roben
thanks
Suraj
what is a sulphate
Alo
any answers
Alo
the time rate of increase in velocity is called
Blessing Reply
acceleration
Emma
What is uniform velocity
Victoria
Greetings,users of that wonderful app.
Frank Reply
how to solve pressure?
Cruz Reply
how do we calculate weight and eara eg an elefant that weight 2000kg has four fits or legs search of surface eara is 0.1m2(1metre square) incontact with the ground=10m2(g =10m2)
Cruz
P=F/A
Mira
can someone derive the formula a little bit deeper?
Bern
what is coplanar force?
OLADITI Reply
forces acting and lying on d same plane
Promise
what is accuracy and precision
Peace Reply
How does a current follow?
Vineeta Reply
follow?
akif
which one dc or ac current.
akif
how does a current following?
Vineeta
?
akif
AC current
Vineeta
AC current follows due to changing electric field and magnetic field.
akif
you guys are just saying follow is flow not follow please
Abubakar
ok bro thanks
akif
flows
Abubakar
but i wanted to understand him/her in his own language
akif
but I think the statement is written in English not any other language
Abubakar
my mean that in which form he/she written this,will understand better in this form, i write.
akif
ok
Abubakar
ok thanks bro. my mistake
Vineeta
u are welcome
Abubakar
what is a semiconductor
Vineeta Reply
substances having lower forbidden gap between valence band and conduction band
akif
what is a conductor?
Vineeta
replace lower by higher only
akif
convert 56°c to kelvin
Abubakar
How does a current follow?
Vineeta
A semiconductor is any material whose conduction lies between that of a conductor and an insulator.
AKOWUAH
what is Atom? what is molecules? what is ions?
Abubakar Reply
atoms are the smallest unit of an element which is capable of behaving as a single unit
Promise
a molecule is d smallest unit of a substances capable of independent existence and can also retain the chemical proper ties of that substance
Promise
an ion is referred to as freely moving charged particles
Promise
Practice Key Terms 4

Get the best College physics course in your pocket!





Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'College physics' conversation and receive update notifications?

Ask