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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 lesers can transmit information
mitul Reply
griffts bridge derivative
Ganesh Reply
below me
please explain; when a glass rod is rubbed with silk, it becomes positive and the silk becomes negative- yet both attracts dust. does dust have third types of charge that is attracted to both positive and negative
Timothy Reply
what is a conductor
Timothy
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Timothy
below me
why below you
Timothy
no....I said below me ...... nothing below .....ok?
dust particles contains both positive and negative charge particles
Mbutene
corona charge can verify
Stephen
when pressure increases the temperature remain what?
Ibrahim Reply
what is frequency
Mbionyi Reply
define precision briefly
Sujitha Reply
CT scanners do not detect details smaller than about 0.5 mm. Is this limitation due to the wavelength of x rays? Explain.
MITHRA Reply
hope this helps
what's critical angle
Mahmud Reply
The Critical Angle Derivation So the critical angle is defined as the angle of incidence that provides an angle of refraction of 90-degrees. Make particular note that the critical angle is an angle of incidence value. For the water-air boundary, the critical angle is 48.6-degrees.
dude.....next time Google it
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Chidalu
pls who can give the definition of relative density?
Temiloluwa
the ratio of the density of a substance to the density of a standard, usually water for a liquid or solid, and air for a gas.
Chidalu
What is momentum
aliyu Reply
mass ×velocity
Chidalu
it is the product of mass ×velocity of an object
Chidalu
how do I highlight a sentence]p? I select the sentence but get options like copy or web search but no highlight. tks. src
Sean Reply
then you can edit your work anyway you want
Wat is the relationship between Instataneous velocity
Oyinlusi Reply
Instantaneous velocity is defined as the rate of change of position for a time interval which is almost equal to zero
Astronomy
The potential in a region between x= 0 and x = 6.00 m lis V= a+ bx, where a = 10.0 V and b = -7.00 V/m. Determine (a) the potential atx=0, 3.00 m, and 6.00 m and (b) the magnitude and direction of the electric ficld at x =0, 3.00 m, and 6.00 m.
what is energy
Victor Reply
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GIDEON
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Bitrus
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faith Reply
what are the basic of physics
faith
base itself is physics
Vishlawath
tree physical properties of heat
Bello Reply
tree is a type of organism that grows very tall and have a wood trunk and branches with leaves... how is that related to heat? what did you smoke man?
algum profe sabe .. Progressivo ou Retrógrado e Acelerado ou Retardado   V= +23 m/s        V= +5 m/s        0__>              0__> __________________________>        T= 0               T=6s
Claudia
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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