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 m^{3} at a temperature of 27 °C and 1 atm

pressure.

__Answer:-__

Volume of the room, V = 25.0 m^{3}

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

Pressure in the room, P = 1 atm = 1 × 1.013 × 10^{5} Pa

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

can be written as:

PV = k_{B}NT

Where,

K_{B} is Boltzmann constant = 1.38 × 10^{–23} m^{2} kg s^{–2} K^{–1}

N is the number of air molecules in the room

N=PV/ K_{B}T

=1.013x10^{5}x25/1.38x10^{-23}x300

= 6.11 × 10^{26} molecules

Therefore, the total number of air molecules in the given room is 6.11 × 10^{26}

__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__

- 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.

- 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)

.