Questions for Thermodynamics (4)

IDEAL GAS LAW, HEAT TRANSFER

  1. How would the P-T graph of a real gas differ from that of an ideal gas? Draw the two graphs on P-T axes.
  2. The root mean square speed of a sample of Helium atoms is 1.36 x 103 m/s. The molar mass of helium is 4g/mol.
    1. What is the temperature of the sample of Helium gas?
    2. Another sample of Oxygen gas is at the same temperature. Treating Oxygen gas as monoatomic, with molar mass 16g/mol, what is the rms speed of the molecules?
    3. Would there be a difference in the rms speed of the Oxygen molecules if they were assumed to be diatomic? And why?

FIRST LAW OF THERMODYNAMICS

  1. One mole of an ideal gas is initially at characteristics P1, V1 and T1. Keeping its temperature constant, it is allowed to expand to three times its initial volume. Express the work done by the gas on the environment in terms of R,T1, P1 and V1.
  2. An ideal gas is kept in contact with a thermal reservoir and allowed to do 60J of work on its surroundings. How much heat flows from the thermal reservoir into the gas?
  3. One mole of a gas is insulated from the environment, and compressed such that 50J of work is done on it. Assume that its molar heat capacity stays constant at 20J/mol. What is its temperature change?
  4. On P-V axes for an ideal gas :
    1. Draw three P-V graphs for three different temperatures, and label them T1 T2 and T3 in order of ascending temperature.
    2. Define a point on the T2 isotherm as the initial characteristics of the gas. Draw the following gas manipulations : Placed in contact with a thermal reservoir, the gas is allowed to expand to twice its volume.
    3. The gas is then compressed to half its volume extremely quickly, such that no heat is exchanged with its surroundings.
    4. The size of the box is now fixed, the gas is placed in contact with a thermal reservoir half its temperature, and allowed to reach equilibrium.
    5. With it pressure kept constant, it is now allowed to expand to 1.5 times its volume.
    6. Shade the area representing the work done by the gas on its surroundings in steps 2 and 5.
  5. Would you predict molar heat capacity at constant pressure or volume to be greater? And why?

HEAT ENGINES, CARNOT CYCLE

  1. A heat engine does 50J of work and expels 100J of energy into its lower temperature reservoir. What is its efficiency? If its lower temperature reservoir is at 100K, what temperature is its higher temperature reservoir at?
  2. A heat engine operating at 80% efficiency takes in 100J of energy. How much energy is used to do useful work? What is the ratio between the temperatures of its low- and high- temperature reservoirs?

SECOND LAW OF THERMODYNAMICS, ENTROPY

  1. When water freezes, its molecules get fixed in a more regular pattern. Why does this not contradict the second law of thermodynamics?
  2. A fridge is turned on and left open in a room for  ten hours. After that, it is turned off and left there for another ten hours. How does the entropy in the room change in the first ten hours and after the second ten hours?
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