



Section summary
 The ideal gas law relates the pressure and volume of a gas to the number of gas molecules and the temperature of the gas.
 The ideal gas law can be written in terms of the number of molecules of gas:
$\text{PV}=\text{NkT},$
where
$P$ is pressure,
$V$ is volume,
$T$ is temperature,
$N$ is number of molecules, and
$k$ is the Boltzmann constant
$k=1\text{.}\text{38}\times {\text{10}}^{\u2013\text{23}}\phantom{\rule{0.25em}{0ex}}\text{J/K}.$
 A mole is the number of atoms in a 12g sample of carbon12.
 The number of molecules in a mole is called Avogadro’s number
${N}_{\text{A}}$ ,
${N}_{\text{A}}=6\text{.}\text{02}\times {\text{10}}^{\text{23}}\phantom{\rule{0.25em}{0ex}}{\text{mol}}^{1}.$
 A mole of any substance has a mass in grams equal to its molecular weight, which can be determined from the periodic table of elements.
 The ideal gas law can also be written and solved in terms of the number of moles of gas:
$\text{PV}=\text{nRT},$
where
$n$ is number of moles and
$R$ is the universal gas constant,
$R=8\text{.}\text{31}\phantom{\rule{0.25em}{0ex}}\text{J/mol}\cdot \text{K}.$
 The ideal gas law is generally valid at temperatures well above the boiling temperature.
Conceptual questions
Find out the human population of Earth. Is there a mole of people inhabiting Earth? If the average mass of a person is 60 kg, calculate the mass of a mole of people. How does the mass of a mole of people compare with the mass of Earth?
Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?
A constantvolume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?
Problems&Exercises
The gauge pressure in your car tires is
$2\text{.}\text{50}\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ at a temperature of
$\text{35}\text{.}0\text{\xba}\text{C}$ when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to
$\u2013\text{40}\text{.}0\text{\xba}\text{C}$ ?
Convert an absolute pressure of
$7\text{.}\text{00}\times {\text{10}}^{5}\phantom{\rule{0.25em}{0ex}}{\text{N/m}}^{2}$ to gauge pressure in
${\text{lb/in}}^{2}\text{.}$ (This value was stated to be just less than
$\text{90}\text{.}{\text{0 lb/in}}^{2}$ in
[link] . Is it?)
Suppose a gasfilled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of
$\text{20}\text{.}0\text{\xba}\text{C}$ . (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is
$\text{60}\text{.}0\text{\xba}\text{C}$ (an approximation) and neglecting any change in volume due to thermal expansion or gas leaks. (b) The actual final pressure for the light bulb will be less than calculated in part (a) because the glass bulb will expand. What will the actual final pressure be, taking this into account? Is this a negligible difference?
(a) 0.136 atm
(b) 0.135 atm. The difference between this value and the value from part (a) is negligible.
Large heliumfilled balloons are used to lift scientific equipment to high altitudes. (a) What is the pressure inside such a balloon if it starts out at sea level with a temperature of
$\text{10}\text{.}0\text{\xba}\text{C}$ and rises to an altitude where its volume is twenty times the original volume and its temperature is
$\u2013\text{50}\text{.}0\text{\xba}\text{C}$ ? (b) What is the gauge pressure? (Assume atmospheric pressure is constant.)
Confirm that the units of
$\text{nRT}$ are those of energy for each value of
$R$ : (a)
$8\text{.}\text{31}\phantom{\rule{0.25em}{0ex}}\text{J/mol}\cdot \text{K}$ , (b)
$1\text{.}\text{99 cal/mol}\cdot \text{K}$ , and (c)
$0\text{.}\text{0821 L}\cdot \text{atm/mol}\cdot \text{K}$ .
(a)
$\text{nRT}=(\text{mol})(\text{J/mol}\cdot \text{K})(\text{K})=\text{J}$
(b)
$\text{nRT}=(\text{mol})(\text{cal/mol}\cdot \text{K})(\text{K})=\text{cal}$
(c)
$\begin{array}{lll}\text{nRT}& =& (\text{mol})(\text{L}\cdot \text{atm/mol}\cdot \text{K})(\text{K})\\ & =& \text{L}\cdot \text{atm}=({\text{m}}^{3})({\text{N/m}}^{2})\\ & =& \text{N}\cdot \text{m}=\text{J}\end{array}$
Questions & Answers
How we are making nano material?
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
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?
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
nano basically means 10^(9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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Source:
OpenStax, Concepts of physics. OpenStax CNX. Aug 25, 2015 Download for free at https://legacy.cnx.org/content/col11738/1.5
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