Question

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.

Short answer

Liquid nitrogen freezes under a vacuum pump because as the pump reduces the pressure, the boiling and freezing points decrease, and the continuous evaporation absorbs heat, eventually lowering the temperature enough to freeze the remaining nitrogen.

Step-by-step solution

Understanding Vapor Pressure

Every liquid has a characteristic vapor pressure, which depends on its temperature. Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase. At boiling point, vapor pressure equals atmospheric pressure, and the liquid can transition into the gas phase.

Effect of Reducing Pressure via a Vacuum Pump

When the vacuum pump is used, the atmosphere inside the container is removed, effectively lowering the pressure. Since the boiling point of a liquid is the temperature at which its vapor pressure equals the surrounding pressure, reducing the surrounding pressure in the insulated container would allow the liquid nitrogen to boil at a lower temperature, thereby cooling it further.

Continued Evaporation and Cooling

As the vacuum pump runs, it continues to remove the gaseous nitrogen that evaporates from the liquid nitrogen. This evaporation is an endothermic process, meaning it absorbs heat. Thus, the temperature of the remaining liquid nitrogen continues to drop as long as the vacuum pump operates.

Freezing of Liquid Nitrogen

Eventually, if the vacuum pump is powerful enough and left on for an extended period, the temperature of the liquid nitrogen can drop below its freezing point. This is because as nitrogen gas is continuously removed, the remaining nitrogen requires energy (heat) to vaporize, which is taken from the thermal energy of the liquid, thus freezing it.

Key concepts

Vapor Pressure

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

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.

Phase Transition

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.

Endothermic Process

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.