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Only quasistatic process can be a polytropic process

  1. Sep 8, 2008 #1
    We may say a process is adiabatic if it occurs fast enough such that no heat is exchanged from the system.But we also say a process is quasi-static when it occurs very slow.

    Then how can PV^gamma = c hold for a fast occuring adiabatic process because a polytropic process should be quasistatic as wiki says http://en.wikipedia.org/wiki/Polytropic_process .

    Also why is it true that only quasistatic process can be a polytropic process.?
  2. jcsd
  3. Sep 8, 2008 #2
    Says who? A process that occurs slowly may be quasistatic but that doesn't necessarily make it so. A quasistatic process is a process that occurs near thermodynamic equilibrium. How the term "near" is described in the last sentence is open to interpretation.

    A quasistatic system is also a system that occurs over several of these near equilibrium states so that eventually the final state is different from the initial state, which can be considered of occurring slowly depending on the amount of the states you want to create for a given process.
  4. Sep 8, 2008 #3
    It is implicitely assumed that throughout the process the thermodynamic variables like tempersture and pressure are well defined, so it has to be a quasi-static process. If you let a gas expand faster and faster, then what will start to happen is that during the expansion process the gas cannot be described by a single set of thermodynamical variables. You'll get a shock wave that propagtes through the gas, so you need to describe the gas using a position dependent temperature, pressure, density, and flow velocity.

    But this description is also just an approximation. If the expansion process is sufficiently violent, local thermodynamic equilibrium will also break down. In that case the velocity distribution of the molecules at any given point in the gas during the expansion process is can no longer be approximated by the Maxwell distribution.

    Such a gas can only be described by a propabaility distribution over velocity and configuration space. The time evolution is given by the Boltzmann equation.
  5. Sep 9, 2008 #4
    So basically can I say even when a process occurs fast, it can be quasistatic if its state can be defined using gas laws. For e.g. the speed of sound has been derived using an adiabatic process , the reason being that the time difference is so small such that no heat is exchanged and then the relation PV^gamma is used. So it means that the state of the air is defined during compression and rarefaction even though these events occur very fast.
  6. Sep 9, 2008 #5
    Yes, but note that the speed of the process which makes the process adiabatic also threatens to make the process not quasistatic. In the case of a soundwave you mention, you have local thermodynamical equilibrium, i.e. at every point in the gas you have a well defined pressure, density and temperature, which evolves adiabatically to a good approximation. But obviously, global thermodynamical equilibrium has broken down: The entire gas cannot be described by a single pressure and temperature. If it could, there wouldn't be a sound wave.
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