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I understand that water boils at lower temperatures at lower pressures, but I want to know what happens when external heat is supplied to a body of water at low pressure. Suppose I have a hot object in an enclosed chamber. I then cover the hot object with water, then vacuum the air out so the pressure drops. I know that with out the help of any additional heat the water can boil at low temperature because i have dropped the pressure, but what happens when I introduce the hot object? Does the water boil even faster because of the exchange of heat between the water and the hot object? What is the boiling point of the water at low pressure and the help of additional heat VS. the boiling point at just vacuum pressure?

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Added heat doesn't change the boiling point, it just makes the water reach it faster. Once it has reached boiling point, the rate of boiling also increases with an increased heat source. Without the hot object, heat is extracted from the remaining liquid body by the vapour that leaves it (enthalphy of vaporization) during boiling, in effect causing evaporative cooling to the rest of the water. This will cause the water to drop below the boiling point eventually unless air pressure is further lowered, or the water is allowed time to absorb heat and warm up (essentially using the environment as an added heat source for boiling). Having a hot object accelerates the process.

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