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Kinetic Theory

  1. Nov 1, 2005 #1
    In the kinetic theory, it is supposed that the molecules make elastic collisions with the walls of the container. Imagine that the collisions were inelastic. Describe and explain the consequence of this with regard to the temperature of the gas.
    So far, i have said that not all of the molecules kinetic energy is conserved and some will be converted into heat causing the temperature of the gas to increase, but i think i need quite a bit more detail for the 6 marks available. Any advice?

    Also, There are no attractive forces between the molecules of an ideal gas. Describe and explain the consequence of this with regard to the two components of internal energy. Can anyone suggest how i would go about answering this?

    Thanx, Katie :smile:
     
  2. jcsd
  3. Nov 1, 2005 #2

    ZapperZ

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    Er.. there's something that doesn't make sense here.

    Heat (and temperature) is a measure of the kinetic energy OF THE GAS! So how could you say that the non-conserved part of the inelastic collision heats up the gas? If this is correct, then you are saying that the missing part goes BACK into the gas kinetic energy, which would mean it is an elastic collision, and so why would it it up all by itself?

    Zz.
     
  4. Nov 1, 2005 #3
    ok point taken, so how do i go about answering the question?
     
  5. Nov 1, 2005 #4
    Hello Katie

    Katie is my girlfriend's name - not checking up on me, are you?

    As ZapperZ said, the temperature of the gas is the gas molecules' kinetic energy. If a collision between a molecule and the wall of the container was inelastic, the molecule will be transferring some energy to the wall, so have a think about the effects of this on the gas, the container and anything the container is in thermal contact with (i.e. its environment).

    As for the question of internal energy, I assume the two components in question are heat and work? I have not thought about this before, but I suppose it would have some effect on the heat capacity of the gas, since supplying heat may not raise the kinetic energies of the molecules (just separate them more) if the interactions were attractive. If the interactions were repulsive, doing work on the gas wouldn't necessarily increase the molecules' kinetic energy either.

    Gotta go. I'll think some more and get back to you.
     
  6. Nov 1, 2005 #5
    thank you, and no i'm not your girlfriend checkin up on you :rofl: much appreciated

    ooh, i have in my notes that the two components of internal energy are kinetic energy and potential energy.
     
    Last edited: Nov 1, 2005
  7. Nov 1, 2005 #6
    All energy supplied to the molecules is converted to kinetic energy, and so increases the temperature of the gas, and none is converted to potential energy since there is no force between the molecules.
     
  8. Nov 2, 2005 #7
    hmm, i was just thinking that if there were no forces between the molecules, then they would not accelerate as they approach / move away from one another so the magnitude of their velocity is constant therefore their kinetic energy is constant?

    also, about my first question, the law of conservation of energy states that energy cannot be created or destroyed, so if no energy is lost to the system, and the molecules lose kinetic energy, will the excess be converted to heat causing the temperature to increase?

    sorry to bother you all again :redface:
     
  9. Nov 3, 2005 #8
    Well, I wouldn't say that the kinetic energy of each molecule would be constant, even if you haven't done statistical mechanics yet. The probability of a given molecule having a given kinetic energy is dependant on what that energy is and what the temperature of the gas is. The long and the short of it is that molecules in a gas have different kinetic energies. Since these molecules collide, they will exchange kinetic energy in these collisions. Remember that an elastic collision is one where the total kinetic energies of the colliding bodies remains unchanged, not individual bodies.

    I would say that, since there are no attractive forces between the molecules, the molecules have no potential energy. All their energy is kinetic, and any increase in energy will lead to an increase in kinetic energy only.

    If a molecule has an inelastic collision with the wall of the container, that molecule will lose kinetic energy to the wall. Since the temperature of the gas as a whole is a function of the sum of the molecules' kinetic energies, this means the temperature of the gas will decrease. The temperature of the wall, the recipient of the 'lost' kinetic energy, will increase. Now, if the hotter wall now just heated up the gas again, it would be no different to modelling the collisions as elastic (in fact, this is probably why we model them as elastic) since the temperature of the gas (i.e. the total kinetic energies of the molecules) would remain constant. However, if the wall loses some of its heat to its environment, the energy is lost from the system permanently, and the temperature of the gas will have decreased.

    Of course, the wall doesn't have to lose heat either to the gas or its environment if it was originally cooler than the gas, but I think ideal gases are generally considered to be in thermal equilibrium with their containers.

    No bother at all. Hope we've helped.
     
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