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

perfect gas.

In Pv = RT

P =Pressure (N/ m^{2}), v =specific volume(m^{3} / 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 0^{0}c and at 1.013 bar (at NTP), the volume of 1kg of air is 0.774 m^{3}

Sample calculation for R for air:

At 0^{0}c and at 1.013 bar (at NTP), the volume of 1kg of air is 0.774 m^{3}

R = PV / mT = (1.013 x 10^{5}) / 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 m^{3} /kg mole

R = PV / T = 1.013 x 10^{5} 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.

R_{02} = 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 10^{23} molecules per gram mole of a substance. This is known as

Avogadro’s number (A).

. . A= 6.023 x 10^{26} 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 / 6.0^{23} x 10^{26}

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