Properties of gases are easier to understand than those of solids and liquids. This is mainly because in a gas, molecules are far from each other and their mutual interactions are negligible except when two molecules collide. The perfect gas equation can be written as PV = µRT where µ is the number of moles and R = NA kB is a universal constant. The temperature T is absolute temperature. Choosing kelvin scale for absolute temperature, R = 8.314 J mol-1K-1. If we fix µ and T in the equation, we get PV = constant i.e., keeping temperature constant, pressure of a given mass of gas varies inversely with volume. This is the famous Boyle's law. Next, if you fix P, shows that V ∝ T i.e., for a fixed pressure, the volume of a gas is proportional to its absolute temperature T (Charles' law).

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CASE_STUDIESEquation of State for Ideal GasEquation of State of a Perfect Gas4 sub-questions

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For an ideal gas, the equation of state is the ideal gas relation PV = µRT. For a fixed amount of the gas i.e. given µ, there are thus, only two independent variables, say P and V or T and V. The pressure-volume curve for a fixed temperature is called an isotherm. The thermodynamic state variables are of two kinds: extensive and intensive. Extensive variables indicate the 'size' of the system. Intensive variables such as pressure and temperature do not. To decide which variable is extensive and which intensive, think of a relevant system in equilibrium, and imagine that it is divided into two equal parts. The variables that remain unchanged for each part are Intensive.

CASE_STUDIESThermodynamic State VariablesEquation of State for Ideal GasIsothermal Process in Thermodynamics