What is an ideal gas? Write the state equation for an ideal gas. Write and explain the different laws relating to gases.

(N/A) An ideal gas is a theoretical model of a gas that satisfies the equation $PV = \mu RT$ at all pressures and temperatures.
No real gas is a perfectly ideal gas.
The provided graph shows the deviation of real gases from ideal gas behavior at three different temperatures. The horizontal line represents the ideal gas,which is parallel to the $P$ (pressure) axis.
All curves approach ideal gas behavior at low pressure and high temperature.
At low pressure and high temperature,the molecules are far apart,and molecular interactions are negligible. Hence,in this limit,a real gas behaves like an ideal gas.
The state equation for an ideal gas is $PV = \mu RT$,where $R$ is the universal gas constant.
Gas Laws:
$(1)$ Boyle's Law: At a constant temperature,the pressure of a given mass of gas varies inversely with its volume.
$\therefore P \propto \frac{1}{V} \implies PV = \text{constant}$.
$(2)$ Charles's Law: At a constant pressure,the volume of a given mass of gas is directly proportional to its absolute temperature.
$\therefore V \propto T \implies \frac{V}{T} = \text{constant}$.
$(3)$ Gay-Lussac's Law: At a constant volume,the pressure of a given mass of gas is directly proportional to its absolute temperature.
$\therefore P \propto T \implies \frac{P}{T} = \text{constant}$.