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Water is put into a corked test tube at 25C. It is heated & the cork pops off. What must have been the min temp reached? Explain.

The question also asks to explain how you could measure this.

I'm having trouble understanding if this is about reaching boiling point or has something to do with critical temp.

So far, this is my reasoning: As temp rises, vapor pressure rises. The water would need to reach a temp of at least boiling point (100 C). At this temp, the vapor pressure of the water would be equal to the external pressure creating a equilibrium inside the tube. Any heat applied after reaching boiling point will increase the pressure inside the tube. The increasing pressure will eventually force the cork to pop and the highly energized water molecules to be released as steam.

I'm also at a loss for how this could be measured. A calorimeter came to mind, but that doesn't seem like it would work. All I can think of is just putting a thermometer inside the test tube and continually reading the temp until the cork pops off. Any suggestions?

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212 degrees fahrenheit is the boiling point for water if I remember correctly. That would be the temperature at which steam and pressure would increase to the point that the cork pops.

You don't need anything more than a thermometer. The volume of the test tube, the amount of water in the test tube and the tightness of the cork will all figure into how long it will take for the cork to pop or the glass to break after the water reaches the boiling point.
212 F or 100 C is the temperature. You don't have to go any higher. The water boils at that point. From then on it's just a matter of time before enough pressure is created.

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A "steam pressure" gauge is the device or instrument to use. The type used in "boilers" to monitor steam pressure. There are formula used to come to the exact figure, (depending on factors like "sea level" or "elevation.)