If I put a pressure sensor inside an airtight container half-filled with water, and heat the water, what will the pressure sensor read as the temperature increases? Would it linearly increase (black line in graph) or sharp incline only after 100C (orange line) or something else? Could one tell the temperature of the water from this measurement?
The curve looks like the yellow line.
This experience is rather famous. It shows the critical point of water. Let's see how it goes.
If the temperature increases, the inner pressure increases a lot inside. At $110$°C, the pressure is about $2$ bars. The mass of the water decreases. But its volume does not change much in the liquid phase, because of the liquid dilatation.
At $180$°C, the pressure is about $10$ bar. The density of the gas increases ($0.0079$ g/mL) and the density of the liquid decreases to $0.87$ g/mL
At $312$°C, the pressure becomes $100$ bars. The liquid density is as low as $0.71$ g/mL. The gas density has increased to $0.046$ g/mL.
The difference density decreases when increasing the temperature.
When the temperature is at $374.8$°C, the pressure is $217$ bars. And both liquid and vapor have the same density $0.31$ g/mL. At this point, suddenly, the limit between the two phases disappears!! There is just one phase inside the container, which can be described as neither a liquid nor a gas, or both simultaneously. This phase is known as the critical phase, and it is both a liquid and a gas. The point $212$ bars, $374.8$°C is called the critical point of water.
At higher temperatures, the water is supercritical, with just one phase.