Compared to the boiling point of water at sea level, how does the boiling point of water change at high altitude hill stations, and what is the correct explanation?

Introduction / Context:
This question arises from basic thermodynamics and everyday observations. People often notice that cooking takes longer in pressure cookers at high altitudes and that water seems to boil at a lower temperature in hill stations. Understanding how atmospheric pressure influences the boiling point of water is essential not only for physics examinations but also for practical reasoning in daily life and engineering applications.

Given Data / Assumptions:
The question compares the boiling point of water at sea level with that at hill stations and offers four descriptive options:
- Same as at sea level
- Less than that at sea level
- More than that at sea level
- Equal to the melting point of ice
It is understood that boiling point is defined as the temperature at which the vapour pressure of a liquid equals the external atmospheric pressure. At higher altitudes, atmospheric pressure is lower than at sea level.

Concept / Approach:
At sea level, where atmospheric pressure is approximately one atmosphere, pure water boils at about one hundred degrees Celsius. As altitude increases, atmospheric pressure decreases. Because boiling occurs when the vapour pressure of water equals the external pressure, a lower external pressure is reached at a lower temperature. Therefore, at hill stations with lower pressure, water boils at a temperature below one hundred degrees Celsius. This means the boiling point is less than that at sea level. The options suggesting that it is the same, higher, or equal to the melting point of ice do not match the physics of phase equilibrium.

Step-by-Step Solution:
Step 1: Recall the definition of boiling point as the temperature at which the vapour pressure of a liquid equals the surrounding atmospheric pressure. Step 2: Recognise that atmospheric pressure decreases with increase in altitude, so pressure at hill stations is lower than at sea level. Step 3: Understand that if external pressure is lower, the vapour pressure of water will equal this external pressure at a lower temperature. Step 4: Conclude that water will boil at a temperature less than one hundred degrees Celsius at high altitudes. Step 5: Select the option that states the boiling point at hill stations is less than that at sea level.

Verification / Alternative check:
An everyday verification is that cooking food by boiling or steaming takes longer at hill stations because the maximum temperature reached by boiling water is lower. Pressure cookers are widely used in such areas to increase the pressure inside the vessel, thereby raising the boiling point closer to or above the sea level value. If the boiling point were higher at high altitude, cooking would become faster without a pressure cooker, which contradicts experience. Similarly, the boiling point cannot be equal to zero degrees Celsius, the melting point of ice, because water remains liquid and does not start boiling at that temperature under normal atmospheric conditions. These practical observations support the conclusion that the boiling point is lower at higher altitudes.

Why Other Options Are Wrong:
Same as at sea level: This ignores the dependence of boiling point on atmospheric pressure and contradicts both theory and practice.
More than that at sea level: If this were true, water would need more heat to boil at higher altitudes, which is opposite to what the pressure and vapour pressure relationship predicts.
Equal to the melting point of ice: This would mean boiling at zero degrees Celsius, which does not occur under normal atmospheric conditions and conflicts with basic phase diagrams of water.

Common Pitfalls:
Some learners mistakenly think that because high altitudes are colder, the boiling point must be higher to compensate, which is not correct. Others assume that boiling point is a fixed property independent of external pressure. To avoid such mistakes, always link boiling to the equality of vapour pressure and external pressure and remember that lower external pressure at high altitudes leads directly to a lower boiling point.

Final Answer:
At hill stations, where atmospheric pressure is lower, the boiling point of water is less than that at sea level.