can anyone explain me the chapter ideal gas equation class11 plz
Answers
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Assumptions of Kinetic Theory of Gases
☺Every gas consists of extremely small particles known as molecules. The molecules of a given gas are all identical but are different from those of another gas.
The molecules of a gas are identical spherical, rigid and perfectly elastic point masses.
☺Their molecular size is negligible in comparison to intermolecular distance (10-9 m).
☺The speed of gas molecules lies between zero and infinity (very high speed).
☺The distance covered by the molecules between two successive collisions is known as free path and mean of all free path is known as mean free path.
☺The number of collision per unit volume in a gas remains constant.
No attractive or repulsive force acts between gas molecules.
☺Gravitational to extremely attraction among the molecules is ineffective due small masses and very high speed of molecules.
Gas laws
☺Assuming permanent gases to be ideal, through experiments, it was established that gases irrespective of their nature obey the following laws.
☺☺☺☺Boyle’s Law☺☺☺☺
At constant temperature the volume (V) of given mass of a gas is inversely proportional to its pressure (p), i.e.,
V ∝ 1/p ⇒ pV = constant
__________
Charles’ Law
At constant pressure the volume (V) of a given mass of gas is directly proportional to its absolute temperature (T), i.e.,
V ∝ T ⇒ V / T = constant
For a given gas, V1/T1 = V2/T2
At constant pressure the volume (V) of a given mass of a gas increases or decreases by 1/273.15 of its volume at 0°C for each 1°C rise or fall in temperature.
Volume of the gas at t°Ce
Vt = V0 (1 + t/273.15)
where V0 is the volume of gas at 0°C.
Gay Lussacs’ or Regnault’s Law
At constant volume the pressure p of a given mass of gas is directly proportional to its absolute temperature T, i.e. ,
p ∝ T ⇒ V/T = constant
For a given gas,
p1/T1 = p2/T2
At constant volume (V) the pressure p of a given mass of a gas increases or decreases by 1/273.15 of its pressure at 0°C for each l°C rise or fall in temperature.
Volume of the gas at t°C, pt = p0 (1 + t/273.15)
where P0 is the pressure of gas at 0°C.
Equation of perfect gas pV=nRT
where p = pressure, V = volume, T = absolute temperature, R = universal gas constant and n = number of moles of a gas.
Universal gas constant R = 8.31 J mol-1K-1.
Real Gases
Real gases deviate slightly from ideal gas laws because
Real gas molecules attract one another.
Real gas molecules occupy a finite volume.
Real or Van der Waal’s Gas Equation
(p + a/V2) (V – b) = RT
where a and b are called van der Waals’ constants.
Pressure due to an ideal gas is given by
p = (1/3).(mn/V). c2 = 1/3 ρ c2
For one mole of an ideal gas
P = (1/3).(M/V).c2
where, m = mass of one molecule, n = number of molecules, V = volume of gas, c = (c12 + c22 + … + cn2) / n allde root mean square (rrns) velocity of the gas molecules and M = molecular weight of the gas. If p is the pressure of the gas and E is the kinetic energy per unit volume is E, then
p = (2/3).E
Degree of Freedom
The degree of freedom for a dynamic system is the number of directions in which it can move freely or the number of coordinates required to describe completely the position and configuration of the system.
It is denoted by for N.
Degree of freedom of a system is given by
f or N = 3A – R
where A = number of particles in the system and R = number of independent relations.
Degree of Freedom
For monoatomic gas = 3
For diatomic gas = 5
For non-linear triatomic gas = 6
For linear triatomic gas = 7
Specific heat of a gas
(a) At constant volume, CV = f/2 R
(b) At constant pressure, cp = (f/2 + 1)R
(c) Ratio of specific heats of a gas at constant pressure and at constant volume is given by
γ = 1 + 2/f
Mean Free Path
The average distance travelled by a molecule between two successive collisions is called mean free path (γ).
Mean free path is given by
γ = kT / √2 π σ2p
where σ = diameter of the molecule, p = pressure of the gas,
T = temperature and k = Botlzmann’s constant.
Mean free path
λ ∝ T and λ ∝ 1/p