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Heat energy change when gas compressed

  1. Jun 11, 2013 #1
    1. The problem statement, all variables and given/known data

    One mole of an ideal gas is in a container with a moveable piston. A 100 N force moves the piston down 1 m; the compression is isothermal.

    Does 100 J of energy leave the gas or enter the gas?

    2. Relevant equations

    W=Fd
    U=Q-W=Q-P(Vf-Vi)

    3. The attempt at a solution

    W=P(Vf-Vi). Since Vf<Vi, Vf-Vi<0, so W<0. Hence U=Q-W=Q+W. Since the compression is isothermal, U=0, so 0=Q+W <=> Q=-W <=> Q=100 J. So 100 J of heat enters the gas.
     
  2. jcsd
  3. Jun 11, 2013 #2
    Because the change in the internal energy is zero, as you rightly indicate, we know that no netto energy enters or leaves the system. This can also be seen from Q = W. The work done by the pressure of the gas is negative. This means that heat is leaving the system during the compression.
     
  4. Jun 11, 2013 #3
    Ok, thanks. If the process weren't isothermal, then heat would enter the gas, right?
     
  5. Jun 11, 2013 #4
    Not necessarily. We can let heat enter or leave the system by bringing it into contact with a source at a higher or lower temperature, or even isolate it and arrange for an adiabatic compression. Both Q and W signifies energy entering or leaving the system. In this case it enters via W and leaves via Q.
     
  6. Jun 11, 2013 #5
    Actually, both. Heat Q and work W are both considered "energy in transit." So 100 J energy enters by doing work on the gas, and leaves by removing heat from the gas.

    Oops. I guess that's the same as Basic_Physics response. Please disregard.

    Chet
     
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