Liquid nitrogen can be used as a cryogenic substance to obtain low temperatures. Under atmospheric pressure, liquid nitrogen boils at 77 \(\mathrm{K}\) , allowing low temperatures to be reached. However, if the nitrogen is placed in a sealed, insulated container connected to a vacuum pump, even lower temperatures can be reached. Why? If the vacuum pump has sufficient capacity and is left on for an extended period of time, the liquid nitrogen starts to freeze. Explain.

Vapor pressure is a vital concept when understanding the behavior of liquids under different conditions. It is the pressure exerted by a vapor that is in equilibrium with its liquid or solid phase. In simpler terms, it's like a tug of war between the molecules in the liquid (or solid) state and those in the gas state. When a liquid reaches a temperature where its vapor pressure equals the surrounding atmospheric pressure, it boils and transitions to a gas. This transition does not happen at a single, fixed temperature; rather, it varies with atmospheric pressure.

For instance, on a high mountain, where the atmosphere is thinner and pressure is lower, water boils at a temperature lower than 100°C. In this context, when using a vacuum pump to remove air and decrease the pressure around liquid nitrogen, the vapor pressure needed to boil the nitrogen also becomes lower. Hence, liquid nitrogen can boil at a lower temperature under reduced pressure, effectively cooling it further due to the enhanced evaporation.

Cryogenics is the branch of physics dealing with the production and effects of very low temperatures. Liquid nitrogen, often used in cryogenics, has a boiling point of 77 K under atmospheric pressure. This allows it to act as a cooling agent. In the world of cryogenics, the ability to reach and maintain extremely low temperatures is crucial, whether for scientific experiments, medical preservation, or industrial applications.

The manipulation of conditions to reach such temperatures involves controlling factors like pressure and isolation from the environment. An insulated container, as used in the exercise, minimizes heat transfer with the surroundings, while a vacuum pump manipulates the pressure to achieve even lower temperatures, pushing the boundaries of how cold the liquid nitrogen can get before it freezes into a solid.

A phase transition is the transformation of a substance from one state of matter to another, such as solid to liquid, liquid to gas, or vice versa. This process occurs when energy, typically in the form of heat, is added or removed from the substance, affecting the movement and arrangement of its molecules.

Each substance has its specific phase transitions at certain temperatures and pressures. These temperatures can be manipulated; for example, by reducing pressure, we can lower the boiling point of a liquid, facilitating a phase transition to gas at a colder temperature. Conversely, by removing energy, as with liquid nitrogen in the exercise, the substance cools and can transition from liquid to solid.

An endothermic process is one that requires an absorption of heat from its surroundings. This is in contrast to an exothermic process, which releases heat. When liquid nitrogen evaporates, it undergoes such an endothermic process. Heat energy from the liquid nitrogen and surrounding environment is absorbed to fuel the transition from liquid to gas, which in turn lowers the temperature of the remaining liquid.

Understanding this principle is key to comprehending why liquid nitrogen can freeze when placed under a vacuum for an extended period. The continued evaporation of nitrogen into a gas causes a drop in the temperature of the residual liquid nitrogen, because it consistently absorbs heat that is no longer being replaced, ultimately leading to the freezing of the liquid once enough heat is lost.