** Write clearly in dark pencil or ink, on one side of the paper only. **
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Constants:
| k = 9*10^9 N m^2 / C^2 | qE = 1.6 * 10^-19 C | h = 6.63 * 10^-34 J s |
| energy of n=1 orbital in hydrogen atom: -13.6 eV | k ' = 9 * 10^-7 T m / amp | atomic mass unit: 1.66 * 10^-27 kg |
| electron mass: 9.11 * 10^-31 kg | speed of light: 3 * 10^8 m/s | Avogadro's Number: 6.023 * 10^-23 particles/mole |
| Gas Constant: R = 8.31 J / (mole K) | proton mass: 1.6726 * 10^-27 kg | neutron mass: 1.6749 * 10^-27 kg |
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Problem Number 1There is a small amount of water at the bottom of a sealed container of volume 8.4 liters which is otherwise full of an ideal gas. A thin tube open to the atmosphere extends down into the water. The system is initially at atmospheric pressure and temperature 277 Celsius.
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Problem Number 2The masses of 1 mole of various gases are as follows: hydrogen about 2 grams, helium about 4 grams, nitrogen about 28 grams, oxygen about 32 grams and carbon dioxide about 44 grams. If the average (rms) molecular speed of oxygen molecules in a mixed gas containing all four of these gases is 293 m/s, then what is the average (rms) molecular speed of molecules of each of the other gases? How much total translational KE is there in a mole of this gas? What other forms of KE might there be in this gas?
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Problem Number 3A tube 3.2 mm in diameter is run through the stopper of a sealed 6-liter container. The tube outside the container forms a U, then runs in a straight line with slope .02 with respect to horizontal. Alcohol is introduced into the tube, and fills the U, extending into the linear section of the tube. Both ends of the tube are open. The container is slightly heated, and the alcohol column is observed to move .88 meters along the linear section of the tube. The material of which the container is constructed has coefficient of linear expansion `alpha = 73 * 10^6 / C. If the temperature of the air in the container was originally 27 Celsius, what is the new temperature?
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Problem Number 4Explain how to use energy considerations to determine the velocity with which water will flow from a hole in a large container if the pressure difference between the inside and outside of the container is 3100 N/m^2, and if the water inside the container is effectively stationary. You may do this symbolically or you may consider the energy changes as a 1-gram mass of water exits the cylinder.
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Problem Number 5Find an expression for the average pressure exerted by N identical particles each of mass m traveling always at speed v on one end wall of a cylindrical container of length L meters and cross-sectional area A m^2, provided the particle travels always along the axis of the cylinder and collides elastically with the ends of the container.
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Problem Number 6What is the difference in blood pressure between the head and feet of a person of height 165 cm?
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Problem Number 7University Physics Problem: Water flows from a hole in a uniform cylinder whose cross-section is a circle of radius .2552 meters. The hole has a radius of .058 meters. Determine the velocity with which water exits the hole when the cylinder is filled to a point 1.3 meters above the hole. Do not assume that the water in the cylinder is stationary.
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Problem Number 8Use Bernoulli's equation to determine the pressure change as water flows through a full horizontal pipe from a point where the pipe diameter is .56 meters and velocity 1.5 m/s to a point where the pipe diameter is .392 meters.
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Problem Number 9Find an expression for the average pressure exerted by a single particle of mass m traveling always at speed v on one end wall of a cylindrical container of length L meters and cross-sectional area A m^2, provided the particle travels always along the axis of the cylinder and collides elastically with the ends of the container.