The Kettle at 2,200 Metres
Ananya, a Class 9 student in Chennai (sea level, atmospheric pressure about 101 kPa), spends a fortnight with her cousin Meera in Shimla (about 2,200 m, atmospheric pressure about 78 kPa). Both houses have identical 1.5-litre electric kettles, and both families use the same brand of bottled water. Ananya measures the water temperature at the moment a rolling boil begins: 100 °C in Chennai, about 92 °C in Shimla, using the same digital thermometer in both places. That evening both families boil eggs in the same way - eggs taken straight from the fridge, placed in cold water, brought to a rolling boil, then simmered. In Chennai the eggs are hard-boiled in about 9 minutes; in Shimla Meera needs nearly 14 minutes for the same result. Meera's mother uses a pressure cooker for dal and finds that it takes 4 whistles in Chennai but 5 in Shimla to reach the same softness. Ananya begins to suspect that her thermometer reads low in the hills.
1. Explain why the water begins to boil at about 92 °C in Shimla. Is Ananya's thermometer faulty?
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No, the thermometer is fine.
A liquid boils when its saturated vapour pressure becomes equal to the external pressure on its surface. At sea level that external pressure is about 101 kPa, and water's vapour pressure reaches 101 kPa at 100 °C. In Shimla the external pressure is only about 78 kPa, and water's vapour pressure climbs to 78 kPa at roughly 92 °C.
So the kettle is genuinely boiling in both places - the bubbles are steam, not air, and they survive all the way to the surface. What has changed is the temperature at which the vapour pressure matches the atmosphere. A reading of 92 °C is exactly what a correct thermometer should show at 2,200 m. The same reasoning explains why a pressure cooker, which raises the external pressure above 101 kPa, cooks faster than an open pot.
2. The water is boiling vigorously in both kitchens, yet the eggs take about 14 minutes in Shimla against 9 minutes in Chennai. Explain, using the idea of reaction rate rather than the idea of 'more heat'.
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Cooking is a set of chemical changes - mainly the denaturation and setting of egg proteins - and the rate of those changes depends on temperature, not on how violently the water bubbles.
At 100 °C the proteins in the egg white and yolk set quickly; at 92 °C the same changes happen, but more slowly, so the egg needs roughly half as much time again. The vigour of boiling only tells you how fast water is turning into steam, which is wasted energy as far as the egg is concerned.
A useful check: the pressure cooker reaches about 120 °C, which is why dal softens in a few whistles. Ranking cooking speed means ranking temperature: 120 °C > 100 °C > 92 °C. Bubbles are not the variable.
3. Meera says: 'If we simply keep the kettle switched on longer, the water will climb past 92 °C to 100 °C and the eggs will cook as fast as in Chennai.' Evaluate this claim.
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The claim is wrong. Once water is boiling in an open vessel, any extra energy supplied goes into the latent heat of vaporisation - it converts liquid water into steam at the same temperature instead of raising the temperature.
The water stays pinned at the local boiling point (about 92 °C in Shimla) while it boils away, so extra heating produces more steam and a faster-drying kettle, not a hotter egg. The temperature could only rise if the pressure on the water were increased, for example by sealing the vessel - which is exactly what a pressure cooker does.
Practical consequence: the only ways to speed up the eggs in Shimla are to raise the pressure, to use a wider/lower pan with less water so the egg's surroundings heat through faster, or to accept the longer time.