Water at 22◦C will spontaneously boil when exposed to a vacuum, for example, if exposed to the atmosphere. Could you cook a hard-boiled egg in this boiling water? Explain your answer.

No, you cannot cook a hard-boiled egg in water boiling at 22°C, even if it is under a vacuum. Here's why:

1. The normal boiling point of water is 100°C at 1 atmosphere of pressure. This is the temperature at which we usually cook food, including hard-boiled eggs.

2. However, the boiling point of water decreases with decreasing pressure. If you reduce the pressure enough (such as in a vacuum), water can boil at room temperature (22°C).

3. Boiling is a phase transition from liquid to gas, and it occurs when the vapor pressure of the liquid equals the external pressure. In a vacuum, the external pressure is very low, so water can boil at a much lower temperature.

4. However, the temperature of the boiling water does not increase beyond its boiling point. So, even though the water is boiling at 22°C in a vacuum, it is still only 22°C hot.

5. The process of cooking an egg involves denaturing the proteins in the egg, which requires a certain amount of heat. The minimum temperature for this to occur is around 60°C. Therefore, water at 22°C, even if it is boiling due to a vacuum, is not hot enough to cook an egg.

6. So, while you can make water boil at 22°C by exposing it to a vacuum, you cannot use this boiling water to cook a hard-boiled egg.