The results of the laws of Boyle and Gas-Lussac can be combined into an expression which represents the relationship between pressure, volume and temperature of a given mass of a gas; such an expression is described as an equation of state.Suppose the gas is in the initial state with volume, V1, pressure p1and temperature T1. We then change the state of the gas to a volume V2, pressure p2 and temperature T2. Let us carry out this change in two steps.
First we change the pressure from p1 to p2 keeping the temperature T1 constant.The resultant volume V2 as given by Boyle’s law is V2=P1V1/P2.
Next, temperature is changed from T1 to T2, keeping the pressure p2 constant. The final volume V2 as given by Charles law is V2T2/T1.It follows that no matter how we change the state of the given amount of a gas, the ratio pV/T always remains constant, i.e. PV/T=K.
The value of K depends on the amount of gas in the system. Since V is an extensive property (which is mass dependent), its value at constant p and T is proportional to the amount of the gas present in the system. Then K must also be proportional to the amount of gas because p and T are intensive properties (which have no mass dependence). We can express this by writing K = nR, in which n is the amount of gas in a given volume of gas and R is independent of all variables and is, therefore, a universal constant. We thus have the general gas law .
pV = nRT.
The universal gas constant R = pV/nT. Thus, it has the unit of (pressure volume) divided by (amount of gas temperature). Now the dimensions of pressure and volume are,.
Pressure = (force/area) = (force/length2) = force length−2.
Volume = length3.
Thus, the dimensions of R are energy per mole per kelvin and hence it represents the amount of work (or energy) that can be obtained from one mole of a gas when its temperature is raised by one kelvin.
Problem based on Gas constant