PHYS260 Practice Exam Questions Sample problems taken from last year s exam that you should understand in preparation for your exam on Monday Please note however the format of your exam will be different from last year s Instead of a combination of short and long questions your exam will consist of four questions with multiple parts ranging in worth from 20 to 30 pts There will be a total of 100 pt for the exam As last year you will be given a table of constants similar to what you see here so your one page sheet should focus on important equations concepts and ideas not constants you generally can look up in a table Again the four questions on your exam will come from Harmonic motion Simple pendulum Fluids Thermodynamics processes PV diagrams Specific Heats Molar C J mol K Substance c in J gm K Aluminum 0 900 24 3 Copper 0 386 24 5 Gold 0 126 25 6 Lead 0 128 26 4 Silver 0 233 24 9 Zinc 0 387 25 2 Mercury 0 140 28 3 Alcohol ethyl 2 4 111 Water 4 186 75 2 Ice 10 C 2 05 36 9 Gases at STP Density gm cm3 Air 0 001293 Carbon dioxide 001977 Carbon monoxide 0 00125 Hydrogen 0 00009 Helium 0 000178 Nitrogen 0 001251 Solids Density gm cm3 Magnesium 1 7 Aluminum 2 7 Density gm cm3 Copper 8 3 9 0 Gold 19 3 1 0000 Iron 7 8 0 998 Lead 11 3 Gasoline 0 70 Platinum 21 4 Mercury 13 6 Uranium 18 7 Milk 1 03 Osmium 22 5 Ice at 0 C 0 92 Liquids Water at Water at 4o C 20o C Substance at 1 atm Melting Point Heat of Fusion Boiling Point Heat to Vaporize Tm K Lf kJ kg Tb K Lv kJ kg Hydrogen 13 8 58 6 20 3 452 Oxygen 54 4 13 8 90 2 213 Nitrogen 63 3 25 5 77 3 201 Ethyl Alcohol 156 104 351 858 Mercury 234 11 3 630 293 Water 273 15 334 373 15 2 256 Lead 600 24 7 2023 871 Aluminum 932 396 2740 10 465 Gold 1336 64 5 2933 1 578 Copper 1359 134 1460 5 065 Iron 1808 289 3023 6 363 Tmelt T freeze Tboil T condense Section I Each problem in this section is worth 10 pts I 1 Starting from the first law of thermodynamics show that if 1 mole of an ideal gas expands adiabatically from an initial temperature Ti to a final temperature Tf the work done by the gas is CV Ti Tf where CV is the molar heat capacity I 2 One mole of an ideal gas undergoes an isothermal expansion from Vi to Vf Derive an expression for the heat flowing into the gas in terms of the temperature and the initial and final volumes I 3 An object hangs from a spring balance and registers 30 N in air 20 N when immersed in water and 24 N when immersed in an unknown liquid What is the density of the unknown liquid I 3 An object hangs from a spring balance and registers 30 N in air 20 N when immersed in water and 24 N when immersed in an unknown liquid What is the density of the unknown liquid I 4 The sewer outlets of a house constructed on a slope are 8 2 m below street level The the city sewer is only 2 1 m below street level What is the minimum pressure differential that must be created by the sewage pump to transfer waste of an average density of 900 kg m3 I 7 A molecular bond can be modeled as a spring between two atoms that vibrate with simple harmonic motion The figure shows a simple harmonic oscillator approximation for the potential energy of an HCl molecule Because the chlorine atom is much more massive than the hydrogen atom it is reasonable to assume that the hydrogen atom m 1 67 10 27 kg vibrates back and forth while the chlorine atom remains at rest What is the frequency Be sure to indicate the values from the graph you are using Section II II 1 A slender uniform metal rod of mass M and length l is pivoted without friction about an axis through its midpoint and perpendicular to the rod A horizontal spring assumed to be massless and with force constant k is attached to the lower end of the rod with the other end of the spring attached to a rigid support Assume that is small enough that the spring remains effectively a Find the torque due to gravity alone 5pts b Find the torque due to the spring 5pts c What is the angular frequency of oscillations of the rod 5pts You might find it helpful to remember that the moment of inertia for a rod pivoting about the center is ml2 12
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