Kinetic Theory Of Gases
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1. Gas Laws
Gas laws are study of any two of quantities like pressure, volume and temperature, when the third is kept constant
A. Boyle's law
- "At constant temperature, the volume of a given mass of gas is invesely propertional to pressure." Thus
V ∝ 1/P
Or, PV = constant (1)
- If P_{1}, V_{1}are initial pressure and volumes and P_{2}, V_{2}be final values then,
P_{1}V_{1}= P_{2}V_{2}
- Graph between P and V at temperature T_{1} and T_{2} such that T_{1}<T_{2} are shown below,
- Graph above shows that Boyle's law is strictly not obeyed by gases at all values of P and T but it obeys this law only at low pressure and high temperature i.e., at law density
B. Charle's Law
- Charle's Law is stated as follows :
"When pressure of a gas is constant the volume of a given mass of gas is directly proportional to its absolute temperature".
V/T = Constant (2)
- Graph between V and T is
This graph shows that experimental graph deviates from straight line. Theoritical and enperimental graphs are in agreement at high temperature.
2. Ideal gas equation
- We can combine Boyle’s law eqn (1) and charle’s law eqn (2) in to a single eqn i.e.,
PV/T = Constant (3)
If n moles is the mass of gas then we write
PV = nRT (4)
where, n is number of moles of gas, R=N_{A}K_{B} is the universal constant known as gas constant and T is the absolute temperature.
- A gas satisfying eqn (4) at all values of presserves and temperatures is said to be an ideal gas
now no of moles of gas
n = m/M = N/N_{A}
where
m - mass of gas containing N molecules
M - molar mass
N_{A} - Avagadro’s number.
From this,
P = ρRT/M
ρ - mass density of gas.
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