It is the gas constant per molecule
\(\therefore { k }_{ B }=\frac { R }{ { N }_{ A } } or\ R={ k }_{ B }{ N }_{ A }\)
R - gas const ; N_A - Avogadro No.;
K_B - Boltzmann
No.of moIecu Ies n =\(\frac{\text {No.of molecules}}{\text {Avogadro's no}}\)=\(\frac{N}{N_A}\)
pv = nRT=\(\frac{N}{N_A}\)K_BN_AT
pv = K_BNT

This-equation gives the relation between pressure  P, volume. (v) and absolute temperature (T) of a gas.
The equation is PV = nRT
n - number of molecules of the gas
R - universal gas constant .
Derivation:
Accumulate the Boyle's law, for a gn mass of a gas at constant temperature.
v\(\times\)\(\frac{1}{p}\) .............(1)
Accumulate to charle's law, for a gn mass of a gas at constant pressure,
V\(\times\)T ................(2) 
Combining (1) & (2)
v\(\times\) \(\frac{1}{p}\) (or) v = constant \(\frac{T}{P}\)(or) \(\frac{pv}{T}\) = constant 
constant is called universal gas constant R.
pv = RT.
For one molecule of a gas, the constant has same value for all gases.
For n moles of a gas pv = nRT.
This is perfect (or) ideal gas equation.

It states that if the pressure remains const, then the v₀ of a g mass of a gas increases or decreases by \(\frac{1}{2723.15}\) of its volume at 0^oC for each 1°C rise or fall of temperature V_o - volume of the g_n mass
of a gas at O°C
Accumulate to charle's law, its volume at 1°C is 
\({ v }_{ 1 }={ v }_{ 0 }+\frac { { v }_{ 0 } }{ 273.15 } ={ v }_{ 0 }\left( 1+\frac { 1 }{ 273.15 } \right) \)
Volume of the gas at t^oC
\({ v }_{ 1 }={ v }_{ 0 }\left( 1+\frac { 1 }{ 273.15 } \right) \)
If T_o and T are temperature on kelvin scale corresponding to 0°C & t^oC, then
T_o= 27:3.15+0 = 273.15
T = 273.15 +t
\(\therefore { v }_{ t }={ v }_{ 0 }\left( \frac { T }{ { T }_{ 0 } } \right) or\frac { { v }_{ 1 } }{ T } =\frac { { v }_{ 0 } }{ { T }_{ 0 } } \)
\(\frac{v}{T}\) = constant i.e. v x T.
So, the law states that at constant pressure the volume of a g_n mass of a gas is directly proportional to its absolute temperature. The graph. between. V and T for a g_n mass of a gas at constant pressure is a S_t line.

 It states that the volume of a gn mass of a gas is inversely proportional to it pressure provided the temperature remains constant.
\(v\times \frac { 1 }{ P } (or)v=\frac { k }{ p } \) (or) pv = constant
Its value depends on
(i) mass of the gas
(ii) its temperature and
(iii) the units in which P and v are measured.
P₁ & V₁ - initial values of pressure and volume
P₂ & v₂ - Final values of pressure and volume
then accumulate the Boyle's law P₁ V₁ = P₂ v₂
Graph between P vs. V and P vs.\(\frac{1}{v}\) for a g_n mass a gas a constant temperature T are shown below.

Consider one mole of an ideal gas enclosed in a cylinder with perfectly non conducting piston.
P₁ - initial pres.
V₁ - initial volume.
T₁ - Initial temperature
A - area of cross-section.
Force excited by the gas on the piston is F = Px A where P - pressure of the gas during expansion.