Estimate at what temperature the water boils in Denver, Colorado : called “the mile high city.” (b) If water boils at 89\deg C, at what elevation are you
The Correct Answer and Explanation is:
Boiling Point of Water in Denver
Water boils at a lower temperature at higher elevations due to the decrease in atmospheric pressure. In Denver, which is located at an altitude of about 5,280 feet (1,609 meters) above sea level, the boiling point of water is lower than the standard 100°C (212°F) at sea level. The decrease in pressure causes the water molecules to require less heat to transition into the vapor phase.
At Denver’s altitude, the boiling point of water is approximately 94°C (201°F), which is lower than the standard boiling point. This is because the atmospheric pressure in Denver is significantly reduced compared to sea level, making it easier for the water molecules to escape as vapor.
Explanation of Boiling Point Decrease:
The boiling point of water is influenced by atmospheric pressure. At sea level, the atmospheric pressure is about 101.3 kPa (kilopascals), which allows water to boil at 100°C. As you ascend in altitude, the atmospheric pressure decreases, meaning that the molecules in the liquid need less energy to escape into the vapor phase, thus reducing the boiling point.
For example, for every 500 feet of elevation gain, the boiling point of water decreases by about 1°F. In Denver’s case, at 5,280 feet, the boiling point is approximately 94°C, which is significantly lower than at sea level. This lower boiling point is an important factor in cooking, as it affects how long it takes to boil water and cook food such as pasta or rice.
b) Elevation Given Boiling Point of 89°C
If water boils at 89°C, we can estimate the elevation using the general rule that for every 1°C decrease in boiling point, the elevation increases by about 500 feet.
- The boiling point at sea level is 100°C.
- The difference between 100°C and 89°C is 11°C.
- Using the rule of thumb, 11°C × 500 feet = 5,500 feet.
Thus, the elevation where water boils at 89°C would be approximately 5,500 feet (1,677 meters) above sea level. This is slightly higher than Denver’s elevation, which is around 5,280 feet. Therefore, the elevation corresponding to a boiling point of 89°C would be located slightly above Denver, but still within the range of high-altitude cities in the Rocky Mountains.
