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Hello. There is something I don't understand about the momentum tensor [itex]t_{ik}=nm\int f(|v|) v_iv_k[/itex] of

an ideal gas with an isotropic velocities distribution where n is the number of molecules per unit volume and m is the

mass of a molecule. Since the the velocity distrubution is isotropic clearly t_ik=0 for i<>k, the problem is that when

i=k we obtein [itex]t_{ii}=1/3nm\overline{v^2}[/itex] which means that if we fix a point in space inside the gas and take some

direction given by a versor n, then an element of surface ds perpendicular to n will experience a momentum flux in same

direction given by n.

The reason why I don't understand this result is because being the velocities distribution isotropic I should find the

same amount of momentun traversing the element of suface in opposite directions thus canceling each other out meaning I should

have t_ik identically zero for all indices. How am I wrong?

an ideal gas with an isotropic velocities distribution where n is the number of molecules per unit volume and m is the

mass of a molecule. Since the the velocity distrubution is isotropic clearly t_ik=0 for i<>k, the problem is that when

i=k we obtein [itex]t_{ii}=1/3nm\overline{v^2}[/itex] which means that if we fix a point in space inside the gas and take some

direction given by a versor n, then an element of surface ds perpendicular to n will experience a momentum flux in same

direction given by n.

The reason why I don't understand this result is because being the velocities distribution isotropic I should find the

same amount of momentun traversing the element of suface in opposite directions thus canceling each other out meaning I should

have t_ik identically zero for all indices. How am I wrong?

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