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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:
    PV = NkT , size 12{ ital "PV"= ital "NkT"} {}
    where P size 12{P} {} is pressure, V size 12{V} {} is volume, T size 12{T} {} is temperature, N size 12{N} {} is number of molecules, and k size 12{k} {} is the Boltzmann constant
    k = 1 . 38 × 10 23 J/K . size 12{k=1 "." "38" times "10" rSup { size 8{–"38"} } " J/K"} {}
  • A mole is the number of atoms in a 12-g sample of carbon-12.
  • The number of molecules in a mole is called Avogadro’s number N A size 12{N rSub { size 8{A} } } {} ,
    N A = 6 . 02 × 10 23 mol 1 . size 12{N rSub { size 8{A} } =6 "." "02" times "10" rSup { size 8{"23"} } `"mol" rSup { size 8{ - 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:
    PV = nRT , size 12{ ital "PV"= ital "nRT"} {}
    where n size 12{n} {} is number of moles and R size 12{R} {} is the universal gas constant,
    R = 8 . 31 J/mol K . size 12{R=8 "." "31"`"J/mol" cdot 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?

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Under what circumstances would you expect a gas to behave significantly differently than predicted by the ideal gas law?

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A constant-volume gas thermometer contains a fixed amount of gas. What property of the gas is measured to indicate its temperature?

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Problems&Exercises

The gauge pressure in your car tires is 2 . 50 × 10 5 N/m 2 size 12{2 "." "50"´"10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {} at a temperature of 35 . 0 º C size 12{"35" "." 0°C} {} when you drive it onto a ferry boat to Alaska. What is their gauge pressure later, when their temperature has dropped to 40 . 0 º C size 12{ +- "40" "." 0°C} {} ?

1.62 atm

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Convert an absolute pressure of 7 . 00 × 10 5 N/m 2 size 12{7 "." "00" times "10" rSup { size 8{5} } " N/m" rSup { size 8{2} } } {} to gauge pressure in lb/in 2 . size 12{"lb/in" rSup { size 8{2} } "." } {} (This value was stated to be just less than 90 . 0 lb/in 2 size 12{"90" "." "0 lb/in" rSup { size 8{2} } } {} in [link] . Is it?)

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Suppose a gas-filled incandescent light bulb is manufactured so that the gas inside the bulb is at atmospheric pressure when the bulb has a temperature of 20 . 0 º C size 12{"20" "." 0°C} {} . (a) Find the gauge pressure inside such a bulb when it is hot, assuming its average temperature is 60 . 0 º C size 12{"60" "." 0°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.

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Large helium-filled 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 10 . 0 º C size 12{"10" "." 0°C} {} and rises to an altitude where its volume is twenty times the original volume and its temperature is 50 . 0 º C size 12{ +- "50" "." 0°C} {} ? (b) What is the gauge pressure? (Assume atmospheric pressure is constant.)

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Confirm that the units of nRT size 12{ ital "nRT"} {} are those of energy for each value of R size 12{R} {} : (a) 8 . 31 J/mol K size 12{8 "." "31"" J/mol" cdot K} {} , (b) 1 . 99 cal/mol K size 12{1 "." "99 cal/mol" cdot K} {} , and (c) 0 . 0821 L atm/mol K size 12{0 "." "0821 L" cdot "atm/mol" cdot K} {} .

(a) nRT = ( mol ) ( J/mol K ) ( K ) = J size 12{ ital "nRT" = \( "mol" \) \( "J/mol" cdot K \) \( K \) =" J"} {}

(b) nRT = ( mol ) ( cal/mol K ) ( K ) = cal size 12{ ital "nRT" = \( "mol" \) \( "cal/mol" cdot K \) \( K \) =" cal"} {}

(c) nRT = ( mol ) ( L atm/mol K ) ( K ) = L atm = ( m 3 ) ( N/m 2 ) = N m = J

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Questions & Answers

how many subject is in physics
Adeshina Reply
the write question should be " How many Topics are in O- Level Physics, or other branches of physics.
effiom
how many topic are in physics
Praise
yh I need someone to explain something im tryna solve . I'll send the question if u down for it
Tamdy Reply
a ripple tank experiment a vibrating plane is used to generate wrinkles in the water .if the distance between two successive point is 3.5cm and the wave travel a distance of 31.5cm find the frequency of the vibration
Tamdy
the range of objects and phenomena studied in physics is
Bethel Reply
what is Linear motion
Hamza Reply
straight line motion is called linear motion
then what
Amera
linear motion is a motion in a line, be it in a straight line or in a non straight line. It is the rate of change of distance.
Saeedul
Hi
aliyu
your are wrong Saeedul
Richard
Linear motion is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimension
Jason
is a one-dimensional motion along a straight line, and can therefore be described mathematically using only one spatial dimensions. 
Praise
what is a classical electrodynamics?
Marga
what is dynamics
Marga
dynamic is the force that stimulates change or progress within the system or process
Oze
what is the formula to calculate wavelength of the incident light
David Reply
if a spring is is stiffness of 950nm-1 what work will be done in extending the spring by 60mmp
Hassan Reply
State the forms of energy
Samzy Reply
machanical
Ridwan
Word : Mechanical wave Definition : The waves, which need a material medium for their propagation, e.g., Sound waves. \n\nOther Definition: The waves, which need a material medium for their propagation, are called mechanical waves. Mechanical waves are also called elastic waves. Sound waves, water waves are examples of mechanical waves.t Definition: wave consisting of periodic motion of matter; e.g. sound wave or water wave as opposed to electromagnetic wave.h
Clement Reply
correct
Akinpelu
what is mechanical wave
Akinpelu Reply
a wave which require material medium for its propagation
syed
The S.I unit for power is what?
Samuel Reply
watt
Okoli
Am I correct
Okoli
it can be in kilowatt, megawatt and so
Femi
yes
Femi
correct
Jaheim
kW
Akinpelu
OK that's right
Samuel
SI.unit of power is.watt=j/c.but kw.and Mw are bigger.umots
syed
What is physics
aish Reply
study of matter and its nature
Akinpelu
The word physics comes from a Greek word Physicos which means Nature.The Knowledge of Nature. It is branch of science which deals with the matter and energy and interaction between them.
Uniform
why in circular motion, a tangential acceleration can change the magnitude of the velocity but not its direction
Syafiqah Reply
reasonable
Femi
because it is balanced by the inward acceleration otherwise known as centripetal acceleration
MUSTAPHA
What is a wave
Mutuma Reply
Tramsmission of energy through a media
Mateo
is the disturbance that carry materials as propagation from one medium to another
Akinpelu
mistakes thanks
Akinpelu
find the triple product of (A*B).C given that A =i + 4j, B=2i - 3j and C = i + k
Favour Reply
Difference between north seeking pole and south seeking pole
Stanley Reply
Practice Key Terms 4

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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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