The Vacuum Chamber Coffee Cup · AI Generator #GEN-C51C7BB4
Physics · thermodynamics
Problem
A materials scientist places a sealed ceramic coffee cup containing hot coffee into a vacuum chamber for an experiment. The cup has a small pinhole in its side that was initially sealed with wax. The coffee is initially at temperature T1=80°C and the cup contains V0=200mL of coffee. The atmospheric pressure outside is P0=1.01×105Pa.
When the vacuum chamber is evacuated, the pressure outside the cup drops to essentially zero. This pressure difference causes the wax seal to fail, and coffee begins to spray out through the pinhole until the pressure inside the cup equals the pressure outside (zero). Assume the coffee behaves as an ideal gas with the same molar mass as water vapor (M=18g/mol), the process happens quickly enough to be adiabatic, and that all the coffee eventually vaporizes and escapes.
What is the final temperature of the coffee vapor just as the last bit exits the cup?