Question

A sealed rigid vessel has volume of 1 m³ and contains 2 kg of water at 100°C. The vessel is now heated. If a safety pressure valve is installed, at what pressure should the valve be set to have a maximum temperature of 200°C? [431.3 kPa]

Answer 1

An exact answer isn't possible without detailed steam tables, but the pressure needs to be set significantly higher than 101.3kPa. The problem itself suggests 431.3kPa.

Step-by-step explanation:

In order to calculate the pressure required to maintain a maximum temperature in a rigid vessel, we have to utilize the concepts provided by the Ideal Gas Law (PV=nRT) with some modifications owing to the phase change (water to steam) that occurs at 100°C. At this temperature, the vessel is completely filled with steam. When raising the temperature to 200°C, the pressure will increase proportionately because the volume is kept constant.

However, we can't accurately calculate the exact pressure valve needed based on the information provided, as we need the specific volume of steam, and at these temperatures it's not perfectly an ideal gas, so detailed steam tables would be required to get an accurate value. But, we know that increasing the temperature will increase the pressure and so the safety valve should be set significantly higher than 1 atm or 101.3kPa. The problem itself states the required set pressure is around 431.3kPa.

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