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IDEAL GAS EQUATION AND ITS LAW

 A hypothetical gas which obeys the law pv* = R*T at all the pressures and temperatures is called an ideal gas. 

Real gases do not conform to this equation of state with complete accuracy. As p =0 , or T = infinity , the real gas approaches the ideal gas behaviour. In the equation, pv* = R*T, as T = 0, i.e, t = 273.15*C 

if  v* remains constant, p=0, or if p remains constant v* = 0. Since negative volume or negative pressure is inconceivable, the lowest possible temperature is 0K or -273.15*C. T is , therefore, known as the absolute temperature.

There is no permanent or perfect gas. At atmospheric condition only., these gases exist in the gaseous state. They are subject to liquefaction or solidification as the temperature and pressure are sufficiently lowered. 

From Avagadro's law, when p= 760 mm Hg = 1.013 * 10^ 5 N/m 2 

T = 273.15 K, an v* = 22.4 m3/ kg mol. 

R* = 1.013 * 10^5 * 22.4 / 273.15 

     = 8314.3 Nm / kg mol K 

     = 8.3143 kJ / kg mol K 

Since v* = V / n , where V is the total volume and n the number of  moles of  the gas, the equation of  state for an ideal gas may be written as 

pV = nR*T 

Also n = m/ u ,

where u is the molecular weight. 

pV = mR*T /u  or 

pV = mRT 

where R = characteristic gas constant = R* / u 

For Oxygen, e.g., 

Ro2 = 8.3143 / 32   =   0.262 kJ / kgK 

for air, '

R air = 8.3143 / 28.96  =  0.287 kJ / kgK 

There are 6.023 * 10^23 molecules in a g mol of  a  substance.

This is known as Avagadro's number (A). 

A = 6.023 * 10^26 molecules / kg mol.

In n kg mole of gas, the total number of  molecules, N, are 

N = nA 

n = N / A 

pV = N R* T / A

      = NKT 

where K = Boltzmann constant 

K = R* / A =  8314.3 / ( 6.023 * 10^26)  = 1.38 * 10^-23 J / molecule K 

There fore, the equation of a state of an ideal gas is given by 

pV = mRT 

      = nR*T 

      = NKT 





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