I first off want to thank you for this channel; the amount of information I am gaining and the intuition you are providing is honestly invaluable! Internal energy is an extensive property, but the probabilistic equation for it does not depend on the number of particles in each state. The equation in the video only evaluates the average energy level/state the particles are occupying, but not the total energy contributed by all the particles. Doesn't that make it an intensive property?
Good question. It depends on whether the energy (Eᵢ) is a per-molecule energy or the energy of the full system. You're right that if the Eᵢ are the energies of individual molecules, then and U will be intensive. If I were being more careful, I could have used a bar (Ū) to indicate that the internal energy is a per-molecule (or per-mole) or intensive quantity. Often, however, you'll need to judge from context whether an energy is intensive or extensive, since it's relatively easy to convert between them by multiplying / dividing by N. Thanks for your comments -- I'm glad you're finding the channel valuable.
so valuable lectures..
I'm glad you're finding them useful
I first off want to thank you for this channel; the amount of information I am gaining and the intuition you are providing is honestly invaluable!
Internal energy is an extensive property, but the probabilistic equation for it does not depend on the number of particles in each state. The equation in the video only evaluates the average energy level/state the particles are occupying, but not the total energy contributed by all the particles. Doesn't that make it an intensive property?
Good question. It depends on whether the energy (Eᵢ) is a per-molecule energy or the energy of the full system.
You're right that if the Eᵢ are the energies of individual molecules, then and U will be intensive. If I were being more careful, I could have used a bar (Ū) to indicate that the internal energy is a per-molecule (or per-mole) or intensive quantity. Often, however, you'll need to judge from context whether an energy is intensive or extensive, since it's relatively easy to convert between them by multiplying / dividing by N.
Thanks for your comments -- I'm glad you're finding the channel valuable.
@@PhysicalChemistry I see, thank you for your help!
Is Q here the molecular partition function or the canonical partition function?