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THERMAL PHYSICS 2
     
    Molar heat capacities of a diatomic ideal gas:
    Cv = 12.5J(molK)-1 and Cp = 20.8J(molK)-1
     
1.   Explain briefly:
  a)  why a gas exerts a pressure
  b)  why the pressure increases with temperature.
     
2. In terms of molecular motion, explain the how evaporation can cause cooling.
    Give an example of a practical use of the phenomenon of cooling by evaporation.
     
3.   In terms of molecular motion, explain why compressing a gas causes its temperature to increase.
    Give an example of a practical use of the increase in temperature caused by compressing a gas.
     
4.   Two cylinders (of negligible heat capacity) each contain 1mol of a gas.
    The gas in each cylinder is heated to increase its temperature by 1K.
    One cylinder is heated at constant volume and the other is heated at constant pressure.
    By considering the quantities of heat supplied to the two cylinders, prove that the following relation is true:
Cp - CV = R
    where Cp is the molar heat capacity at constant pressure, CV  is the molar heat capacity at constant volume and R is the universal gas constant.
     
5.   Two experiments were done attempting to verify the Boyle-Marriotte law.
    The graphs below were obtained.
   
    In each case the broken line indicates (approximately) the expected result.
    Unfortunately, neither of these graphs verifies the law.
    What is the most probable reason for the failure of each experiment?
     
6.   Two moles of an ideal gas are heated at a constant pressure of 105Pa.
    The temperature of the gas increases from 293K to 313K.
    Calculate:
  a) the quantity of thermal energy supplied during the heating process
  b) the change in internal energy of the gas
  c) the work done by the gas during expansion
  d) the change in volume of the gas.
     
7.   20mols of an ideal gas are in a cylinder of initial volume 0.5m3 at a temperature of 27C.
    The gas is supplied with 10000J of heat at constant pressure.
    Calculate:
  a) the final temperature of the gas
  b) the final volume of the gas
  c) the change in internal energy of the gas
     
8.   A cylinder has a volume, V, and contains 2.0010-2mols of oxygen (behaving as an ideal gas) at 20C and 1.00105Pa.
    The gas is compressed rapidly into a volume V/25.
    The pressure of the gas increases to 9.06106Pa
a) The volume of the has gas been made 25 times smaller.
    Why has the pressure increased by more than 25 times?
  b) Calculate the temperature of the compressed gas assuming that no thermal energy entered of left the gas during the compression.
  c) Calculate the volume of the cylinder, V.
  d) If the internal energy of 1mol of oxygen is increased by 12.5J, then the temperature of the gas will increase by 1K.
    Use this fact to calculate the work done during the compression.
     
9.   Draw diagrams to represent:
  a) a heat engine
  b) a heat pump (or fridge)
    On the diagrams, label the work done, w, the energy taken from the source, Q1 and energy given to the sink, Q2.
     
10.   Referring to your diagrams of the previous question, write down expressions for the thermodynamic efficiency of:
  a) a heat engine
  b) a heat pump
  c) a fridge
     
11.   A heat engine is used to lift a mass of 200kg.
    The mass moves 10m vertically upwards.
    The temperature of the source of the heat engine is 1000K and the heat sink is the atmosphere at 293K.
    Ignoring friction in the engine, pulleys etc, calculate the minimum quantity of thermal energy needed to lift the mass.
 
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