Inversion temperature is defined as the temperature above which a gas gets warm up and below which, the gas become cooler, when expanded adiabatically. Boyle temperature for a gas is \(20^{\circ} \mathrm{C}\). What will happen to the gas if it is adiabatically expanded at \(50^{\circ} \mathrm{C}\) ? (a) Heating (b) Cooling (c) Neither heating nor cooling (d) First cooling then heating

Understanding adiabatic expansion is key to grasping many phenomena in thermodynamics. It refers to a process in which a gas expands without exchanging heat with its environment. This might initially sound puzzling: How can the gas's volume increase without a heat transfer?

When a gas undergoes adiabatic expansion, its particles do work to push against the external pressure, and as a result, their kinetic energy decreases. If a gas expands at a temperature above its inversion temperature, it absorbs energy from the work done during expansion and heats up. On the other hand, below the inversion temperature, the gas would cool down as it does work on its surroundings.

This behavior ties directly into our problem, where we consider a gas initially at a higher temperature than its Boyle temperature undergoing expansion.

The Boyle temperature is a unique point for a gas where its pressure is directly proportional to volume, following Boyle's Law, but only at this specific temperature. More formally, it marks the condition under which a real gas behaves like an ideal gas, and the intermolecular forces are effectively 'cancelled out' for changes in volume at constant temperature.

In the context of our problem, knowing the Boyle temperature of a gas helps us determine how it will behave when adiabatically expanded. If expanded at a temperature above the Boyle temperature (which we established is equal to the gas's inversion temperature), the gas will experience heating, which in our case happens at the higher temperature of 50 degrees Celsius.

The behavior of gases under various conditions of temperature, pressure, and volume is governed by gas laws. These laws are crucial for understanding the fundamentals of thermodynamics and how gases react to different physical situations.

Key gas laws include Boyle's Law, which states that pressure inversely varies with volume at constant temperature; Charles's Law, connecting volume and temperature at constant pressure; and Gay-Lussac's Law, relating pressure and temperature at constant volume. Each of these describes how one particular property of a gas will change, holding the others steady.

In our scenario, Boyle's Law is of particular importance as it lays the foundation for understanding the Boyle temperature concept. As gas laws are often idealized, discussing the inversion temperature further provides insight into how real gases deviate from these ideal relationships.

Thermodynamics is the branch of physics that deals with the relationships between heat and other forms of energy. In our exercise, thermodynamics helps us predict the outcome of adiabatic processes among other heat-related transformations.

Four main laws of thermodynamics lay the foundation for energy and heat transfer analysis. The first law, essentially the law of energy conservation, states that energy can neither be created nor destroyed, only transformed. This law is particularly relevant in adiabatic processes, as the internal energy change of a gas is equal to the work done on or by the gas since no heat is exchanged.

Our study of inversion temperature dips into the heart of thermodynamics, combining concepts of energy, work, and heat transfer, to explain why a gas would heat up or cool down when adiabatically expanded at different temperatures.