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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

Explain why magnetic damping might not be effective on an object made of several thin conducting layers separated by insulation? can someone please explain this i need it for my final exam
anas Reply
Hi
saeid
hi
Yimam
What is thê principle behind movement of thê taps control
Oluwakayode Reply
what is atomic mass
thomas Reply
this is the mass of an atom of an element in ratio with the mass of carbon-atom
Chukwuka
show me how to get the accuracies of the values of the resistors for the two circuits i.e for series and parallel sides
Jesuovie Reply
Explain why it is difficult to have an ideal machine in real life situations.
Isaac Reply
tell me
Promise
what's the s . i unit for couple?
Promise
its s.i unit is Nm
Covenant
Force×perpendicular distance N×m=Nm
Oluwakayode
İt iş diffucult to have idêal machine because of FRİCTİON definitely reduce thê efficiency
Oluwakayode
if the classica theory of specific heat is valid,what would be the thermal energy of one kmol of copper at the debye temperature (for copper is 340k)
Zaharadeen Reply
can i get all formulas of physics
BPH Reply
yes
haider
what affects fluid
Doreen Reply
pressure
Oluwakayode
Dimension for force MLT-2
Promise Reply
what is the dimensions of Force?
Osueke Reply
how do you calculate the 5% uncertainty of 4cm?
melia Reply
4cm/100×5= 0.2cm
haider
how do you calculate the 5% absolute uncertainty of a 200g mass?
melia Reply
= 200g±(5%)10g
haider
use the 10g as the uncertainty?
melia
which topic u discussing about?
haider
topic of question?
haider
the relationship between the applied force and the deflection
melia
sorry wrong question i meant the 5% uncertainty of 4cm?
melia
its 0.2 cm or 2mm
haider
thank you
melia
Hello group...
Chioma
hi
haider
well hello there
sean
hi
Noks
hii
Chibueze
10g
Olokuntoye
0.2m
Olokuntoye
hi guys
thomas
the meaning of phrase in physics
Chovwe Reply
is the meaning of phrase in physics
Chovwe
write an expression for a plane progressive wave moving from left to right along x axis and having amplitude 0.02m, frequency of 650Hz and speed if 680ms-¹
Gabriel Reply
how does a model differ from a theory
Friday Reply
To use the vocabulary of model theory and meta-logic, a theory is a set of sentences which can be derived from a formal model using some rule of inference (usually just modus ponens). So, for example, Number Theory is the set of sentences true about numbers. But the model is a structure together wit
Jesilda
with an iterpretation.
Jesilda
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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