The mathematical expression of the ideal gas law is \( \begin{array}{l}P V=n R T \\ \frac{P_{1}}{V_{1}}=\frac{P_{2}}{V_{2}} \\ P_{1} V_{1}=P_{2} V_{2} \\ P_{T}=P_{1}+P_{2}+P_{3} \\ \frac{P_{1}}{T_{1}}=\frac{P_{2}}{T_{2}} \\ \text { Submit Request Answer }\end{array} \)

The ideal gas law, expressed as \( PV = nRT \), has roots going back to the late 19th century when scientists like Boyle, Charles, and Avogadro formulated foundational concepts of gas behavior. These pioneers effectively captured how gases expand, contract, and change pressure under various temperature conditions, leading to the unifying equation we cherish today. It's fascinating how these early insights continue to be essential in fields ranging from chemical engineering to environmental science! In the real world, the ideal gas law is essential in various applications, such as calculating how gas behaves in engines and understanding the atmosphere's dynamics. For example, meteorologists use it to predict how air pressure changes with altitude, helping to forecast weather patterns. Plus, engineers often rely on the ideal gas law to design everything from air conditioning systems to high-performance engines, demonstrating the law's wide-reaching influence!