1) A small sealed chamber (volume 0.10 m3 ) is located below a large water tank, as shown in the diagram. The tank is full of water at 20.0oC, the water is 4.0 m deep, and the air pressure above the tank is 1.0 atm. Initially there is a vacuum inside the chamber. Due to rust, a small hole opens up in the bottom of the tank, allowing water to flow into the chamber.
a) Assuming water is an ideal fluid, what is the speed of the water coming out of the hole? Calculate the water speed when the chamber still contains a vacuum.
b) The water entering the chamber falls onto a heater, which turns the water into steam (water vapor) at 100.0oC. As a result, the pressure in the chamber rises. How large must the pressure in the chamber be, so that water stops flowing through the hole? (Give the absolute pressure in Pa, not the gauge pressure.)
c) How many moles of water vapor in the chamber are needed in order to get the pressure found in part b? What is the mass of this amount of water?
d) How much heat, in J, did the heater need to provide in order to vaporize the water?
Data: Acceleration due to gravity g = 9.81 m/s2
Universal gas constant R = 8.31 J/Kmol = 0.0821 Latm/Kmol
Molecular weight of water = 18.0 (atomic mass units or g/mol)
Heat of vaporization for water Lv = 2257 kJ/kg Density of water = 1000.0 Kg/m3
Specific heat of water = 4184 J/kgK =1.00 cal/goC 1 cal = 4.184 J 1 atm = 101.3 kPa
Zero of Celsius scale = 273.15 K