They are not the same, but related. From Wikipedia (article "gas constant"): " [The gas constant] is equivalent to the Boltzmann constant, but expressed in units of energy (i.e. the pressure-volume product) per temperature increment per mole (rather than energy per temperature increment per particle)".
Boltzman constant
No, the gas constant, or any constant, is constant meaning it doesn't change.
Boltzmanns constant
"Characteristic Gas Constant"The constant 'R' used in the characteristic gas equation PV=RT , has a constant value for a particular gas and is called 'Characteristic gas constant' or 'specific gas constant' . Its value depend upon the temperature scale used and the properties of the gas, under consideration.The value of R will be.For atmospheric pressure air,R= 287 J/kg/k
a simple model that describe the distribution of velocity of molecules in a gas with probabality concept. according to this model the probability of finding a certain velocity in a gas is proportional to e-E/KT, where E=1/2 mv2 for a free atoms of a gas.
The Boltzman's constant is the physical constant relating to temperature to energy.
Boltzman constant
Each molecule of gas have enery = 0.5KT where T is the absolute temperature in Kelvin and K is the Boltzman's constant.
The gas constant is the same for all gases: R = 8,314 462 1(75) J/mol.K
The average translational kinetic energy of particles in a plasma is 3kT/2, i.e. the equation for kinetic energy of plasma particles is the same as any other form of matter. In this respect, a plasma is not significantly different from a gas. The average kinetic energy is directly proportional to the temperature. In a real sense, kinetic energy at the molecular level and temperature at the macro level are the same thing; quantities like the universal gas constant (R) and Boltzman's constant (k) can be viewed as simply unit conversion factors between degrees and joules.
The gas constant (R) makes both sides of the ideal gas equation (PV=nRT) equal. It is therefore called the proportionality constant in the ideal gas equation. The value of R is 8.314 J/mol˚K. If you divide the ideal gas constant by Avogadro's number you get R/NA=(8.314 J mol-1 K-1)/(6.022x1023 #of atoms mol-1)=1.38x10-23 J/(atoms x K) since the mol-1 terms cancel out. This value is the Boltzman constant (kb) usually expressed in units of J/K (energy/temperature) and it gives the average energy of a single atom or molecule at an absolute temperature T. Just multiply kb by T and you get energy in Joules.
If the gas is contained at a constant volume, the pressure increases. If the gas is not contained, the pressure remains the same or drops.
It will increase? No it will decrease when the same amount of gas is held at constant temperature.
No, the gas constant, or any constant, is constant meaning it doesn't change.
The concept of increased temperature calling for an increase in volume to maintain constant pressure can be found in the combined and/or ideal gas law. The combined gas law is PV=kNT, where P is pressure, V is volume, k is Boltzman's constant, N is number of gas molecules and T is temperature. The ideal gas law is PV=nRT where P is pressure, V is volume, n is number of moles of gas, R is gas constant and T is temperature. In both cases a rise in T would call for a rise in V to maintain constant P.
One is for constant pressure, the other is for constant volume. These are not the same; for example, if the pressure is maintained constant, and the gas is heated, the volume changes.
At isobaric (pressure) expansion (volume increase) the temperature will increase because V is proportional to T for the same amount of gas (closed container) at constant pressure.