The gas constant is a number. It is measured in terms of energy per temperature increase per mole. It has no specific volume.
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The pressure increases as well.
Directly proportional, at pressure and temperature constant.
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)".
I suppose you mean the formula for the variation in pressure. The simplest expression of this is, at a fixed temperature,and for a given mass of gas, pressure x volume = constant. This is known as Boyle's Law. If the temperature is changing, then we get two relations: 1. If the pressure is fixed, volume = constant x temperature (absolute) 2. If the volume is fixed, pressure = constant x temperature (absolute) These can be combined into the ideal gas equation Pressure x Volume = constant x Temperature (absolute), or PV = RT where R = the molar gas constant. (Absolute temperature means degrees kelvin, where zero is -273 celsius)
Gay-Lussac's law