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Ideal Gas or Perfect Gas

A gas which follows Pv = RT at all pressures and temperatures is called an ideal or

perfect gas.

In                                 Pv = RT

P =Pressure (N/ m2), v =specific volume(m3 / kg ) ·

R = Gas constant which depends on type of gas. (J /kg K)

T = Absolute temperature (K).

 

If the mass of the gas is 111 (kg), then it can be included in equation (9.1) by following.

u  = V /m

where                                      V = volume of m kg of gas ( m3)

(9.1)                                 p.v/m = RT

PV = Mrt

 

Equation (9.2) can also be called ideal gas equation of state.

Unit of R:                    R = PV / mT

Sample calculation for R for air:

At 00c and at 1.013 bar (at NTP), the volume of 1kg of air is 0.774 m3

Sample calculation for R for air:

At 00c and at 1.013 bar (at NTP), the volume of 1kg of air is 0.774 m3

R = PV / mT = (1.013 x 105) / 1 x 273.15 = 287 Nm / kg k

Multiplying equation (9.1) both sides by M (molecular weight of the gas), we get

MPv = MRT [v is the volume per unit mass of the gas]

or                     P (Mv) = (MR) T

or                            PV = RT

where                      V = Mv = molar volume

and                          R = MR

As per Avogadro’s hypothesis; V is same for all gases at NTP and therefore R must also be same for all gases. This constant R which has the same value for all gases is known as universal gas constant and it does not depend upon the type of gas.

 

S.I. Unit of R:

R = MR=J/kg mole K.

S.I. Value of R :

V = 22.4 m3 /kg mole

R = PV / T = 1.013 x 105 x 22.4 / 273.15 = 8307 j /kg mole k = 9314.3 J / kg mole k

Now the R can be calculated from equation R = R /M.

R02 = 8.3143 / 32 Kj / kg k.

= 0.269 kj /kg k = 0.262 kj / kg k.

R air = 8.3143 /28.96 = 0.287 kj / kg k.

There are 6.023 x 1023 molecules per gram mole of a substance. This is known as

Avogadro’s number (A).

. .                                             A= 6.023 x 1026 molecules I kg mol.

 

The universal gas constant divided by A is called the Boltzman constant and denoted

By K.

K = R / A = 8314.3 / 6.023 x 1026

= 1380 x 10 -26 = 13.8 x 10 -24 j / molecule k.