Volume expansion coefficient of water: 207 e-6/k; Bulk modulus: 2.2GPa. If the deformation of the cup is ignored, the pressure change from 95C to 20C is -75 K * 2.2GPa * 207E-6/K = 34MPa.
The reason why the deformation of the cup is ignored is because the expansion coefficient of glass is about one tenth of that of water; The bulk modulus is about dozens of times that of water.
In addition, the atmospheric pressure is about 0. 1MPa, which is much less than 34MPa. Therefore, if no bubbles are formed, a tensile stress of 34MPa will be generated in water.
The tensile strength of water (that is, the maximum tensile stress before bubble generation) is less than 34MPa (see Yun Guan and D.G. Fredlund's paper, CAN. Geological technology. j . 34:604–6 14( 1997)。 So the tensile stress in water does form bubbles. This process of forming bubbles is called nucleation. Nucleation should occur before the temperature drops to 20℃.
After bubble nucleation, the tensile stress in water will decrease rapidly; Eventually it will become compressive stress because of saturated vapor pressure. In the case of bubble formation, the pressure of water is exactly equal to its saturated vapor pressure. The saturated vapor pressure of pure water at 20 degrees Celsius is 2.3KPa.
This 2.3KPa is far less than 0. 1MPa of atmospheric pressure.
Conclusion: You are basically right. If the temperature drops to 20C, the air pressure in the cup will be very low. Although it is not zero, it is far less than atmospheric pressure. 、
In addition, the saturated vapor pressure of water at 60C is about 20KPa. This is about 1/5 of atmospheric pressure.