Class 11 Physics Kinetic Theory Ideal Gas

Ideal Gas

  • A gas that satisfies the perfectgas equation exactly at all pressures and temperatures.
  • Ideal gas is atheoretical concept.
  • No real gas is truly ideal.A gas which is ideal is known as real gas.
  • Real gases approach the ideal gas behaviour for low pressures and high temperatures.

Problem:-

Estimate the total number of air molecules (inclusive of oxygen, nitrogen, water vapour

and other constituents) in a room of capacity 25.0 m3 at a temperature of 27 °C and 1 atm

pressure.

Answer:-

Volume of the room, V = 25.0 m3

Temperature of the room, T = 27°C = 300 K

Pressure in the room, P = 1 atm = 1 × 1.013 × 105 Pa

The ideal gas equation relating pressure (P), Volume (V), and absolute temperature (T)

can be written as:

PV = kBNT

Where,

KB is Boltzmann constant = 1.38 × 10–23 m2 kg s–2 K–1

N is the number of air molecules in the room

N=PV/ KBT

=1.013x105x25/1.38x10-23x300

= 6.11 × 1026 molecules

Therefore, the total number of air molecules in the given room is 6.11 × 1026

Real gases deviation from ideal gas

  • Real gases approach the ideal gas behaviour for low pressures and high temperatures.
  • Ideal gas equation PV=μRT, for 1 mole ,μ=1,PV=RT
  • =>PV/RT=constant
  • Graph should be a straight line(parallel to x-axis) for ideal gas.
  • This means it has constant value at all temperature and all pressure.
  • But in case of real gases graph approach ideal gas behaviour at high temperature and low pressure.
  • At high temperature and low pressure molecules are far apart. When temperature is increased the molecules will move randomly far from each other.
  • As a result molecular interaction decreases the gas behaves as an ideal gas.
  • The ideal behaviour comes into picture when the molecular present inside the gas don’t interact with each other.

 

Real gases approach ideal gas behaviourat low pressures and high temperatures.

Deduction of Boyle’s law and Charles law from perfect gas equation

  1. Boyle’s law: -Deriving Boyle’s law from perfect gas equation, PV=μRT
  • Consider T (temperature) and μ (no. of moles) constant.
  • Therefore PV=constant.
  • According to Boyle’s law, at a constant temperature, pressure of a given mass of gas varies inversely with volume.
  1. Charles’s law:-Consider If P(Pressure) is constant, then
  • From Perfect gas equation PV =μRT,=> V/T=μR/P =constant
  • Therefore V/T = constant.
  • According to Charles’s law for a fixed pressure,volume of a gas is ∝to its absolute temperature.
  • Conclusion: - Ideal gas satisfies the Boyle’s law and Charles’s law.

 

Experimental P-V curves (solid lines) forsteam at three temperatures comparedwith Boyle’s law (dotted lines). P is in unitsof 22 atm and V in units of 0.09 litres.

 

(Boyle’s law)

 

(Charles’s law)

 

(Gay-Lussac law)

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