Final answer:
The boiling point of water decreases with higher altitude due to lower atmospheric pressure, while the freezing and melting points remain constant. Cooking times are increased because water boils at a lower temperature. Pressure cookers help counteract this effect by increasing the pressure and thus the boiling point inside the vessel.
Step-by-step explanation:
At an altitude of 5,000 meters, the freezing point and melting point of water remain unchanged at 0°C; however, the boiling point is affected by the lower atmospheric pressure and is lower than 100°C, the boiling point at sea level. Although a precise boiling point at this altitude isn't provided here, for elaboration, at 1,500 meters (approximately 5,000 feet), water boils at about 95°C, and at higher altitudes, such as 5,000 meters, the boiling point would be even lower.
Altitude affects the boiling point of water because the air pressure decreases as altitude increases. With reduced atmospheric pressure, less energy is required for water molecules to escape the liquid phase and become gas, thus leading to a decrease in boiling temperature. This concept explains why pasta takes longer to cook in the mountains, because at a lower boiling temperature, water has less heat energy to transfer to the pasta, increasing cooking time. A pressure cooker is useful because it allows food to be cooked under higher pressure, raising the boiling point of water inside the cooker, thereby cooking food more quickly.