Thought provoking problems on heat and thermodynamics

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These problems are from pre-test conducted in teacher's workshops by Prof HC Verma and his team.

Test 1

Source: RESPECT KV MRP Workshop 15th-24th May 2017
  1. Which of these is a function of the state of a gas?
    1. Heat $Q$
    2. Work $W$
    3. Internal energy $U$
    4. $U+PV$
  2. The figure shows adiabatic processes for samples of equal moles of three gases. Write the name of one possible gas for each of the three processes. Process-1 gas:__________. Process-2 gas:_________. Process-3 gas:_______
  3. Consider isothermal expansion of an ideal gas.
    1. If the gas does a work W, how much heat Q is given to the gas?
    2. Is the heat Q completely converted into work in this process?
    3. Is this a violation of the 2nd law of thermodynamics?
  4. Consider the following gas systems all at room temperature. In which case $|pV-nRT|$ will be smallest and in which case it is largest?
    1. gas in an LPG cylinder
    2. hydrogen gas filled in a balloon which tries to go up in atmosphere
    3. air in your water bottle
    4. air in the tubes of a car
  5. A suit of a hotel has two identical rooms connected by a door. The living room is air conditioned and is set at 24 deg C while the outer room has no air conditioning. Suppose the door remains open for quite some time. Which of the rooms will have more air if it is
    1. a hot summer day (outside temperature 45 deg C),
    2. a chill winter night (outside temperature 5 deg C)?
  6. Consider an air molecule in a closed plastic box. What is the order of distance moved by this molecule in an hour?
    1. 1 km
    2. 10 km
    3. 100 km
    4. 1000 km
    5. 10000 km or more
  7. Two processes $AB$ and $A^\prime B^\prime$ on a sample of ideal gas are shown on volume vs temperature diagram. In which of the two processes, the work done by the gas is larger? Give a one-sentence justification.
  8. A gas is suddenly compressed. During the process what kind of relation between the pressure and the volume should be used?
  9. Most of the solids expand on increasing temperature. This is because
    1. Some of the atoms leave the lattice site at higher temperature
    2. The vibration amplitudes of the atoms increase at higher temperature
    3. The inter-atomic potential energy is not symmetric about the minimum energy
    4. The electrons go to larger orbits.

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