Compressed air in the tube of a bicycle wheel at normal temperature suddenly starts coming out from a puncture. The air inside:

  • A
    Starts becoming hotter
  • B
    Remains at the same temperature
  • C
    Starts becoming cooler
  • D
    May become hotter or cooler depending upon the amount of water vapour present

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By what factor should the volume of an ideal gas $(\gamma = 1.5)$ be increased through an adiabatic expansion so that its $rms$ speed becomes half?

For an adiabatic process,if $\gamma = 2.5$ and the volume becomes $1/8$ of its initial volume,then the new pressure $P'$ is (initial pressure $= P$):

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