Chemical Thermodynamics 3.8 - Statistical Heat and Work

Short physical chemistry lecture on reversible heat and work in statistical mechanics.
The change in internal energy in closed systems leads to an expression in statistical mechanics which can be compared to macroscopic results to derive equations for heat and work in reversible processes from the perspective of statistical mechanics.
Notes Slide: i.imgur.com/BJzA1n0.png
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[@happagasa4825]

Hey Here,Can anyone tells me the different btn average internal energy and the usual internal energy

[@nkyu3035]

if the energy of ideal gas is primarily from translational E which has a value of 3/2nRT, how come the energy is dependent on N and V?
even if I look through Q_trans from system partition function, it's dependent on N, V and T.
about the title at the top of the left side of the screen, did you mean macroscopic?

[@TMPChem]

Because at constant E only 2 out of the 3 variables N, V, and T are independent. If you pick two of them, the 3rd one can be calculated exactly (and if that wasn't true, then you don't have an ideal gas). This works in exactly the same way as PV = nRT, how picking any 3 of the 4 (P, V, n, T) allows you to calculate the 4th exactly. In fact, saying that the total energy of a gas is 3/2 nRT is equivalent to saying it's an ideal gas (i.e. PV = nRT).

[@nkyu3035]

haha; I thought I understood. now I'm more confused.
why are you talking about constant E and independent variables?
doesn't eqn E=E(N,V) mean the E is dependent on N and V? not that the E is constant and independent of N and V?
when I think about Q, E should be E(n,V,T).
but since the E equals 3/2nRT(=3/2PV), E shuld be E(n,T) or E(P,V).
it's a disaster -_- help me!

[@nkyu3035]

1) It kept me confused so I came up with another idea.
E_i, which is the energy of state, is equal to h^2/8ml^2((n_x)^2+(n_y)^2+(n_z)^2). So it can be said E_i is a function of (n, l) or (n,V).
Does it work?
2) In your comment on this video, you said work changes the energy levels but keeps the probabilities constant.
p_i is a function of E_i and T. So how can we say work doesn't change probability?

[@SoumilSahu]

Isn't dq dependent on volume? I mean does it not have a dv term as well?

[@TMPChem]

Since we determined which term corresponds to dw, and since dU = dw + dq, therefore dq must equal the remaining term. As you mentioned, this term does not depend on volume, but it does depend on temperature. Heat is an input of thermal energy into the system. Depending on the heat capacity, that will have some effect on the temperature. Depending on the energy levels and temperature, this will have some effect on the probabilities. The main takeaway of this video is that work changes the energy levels but keeps the probabilities constant, while heat changes the probabilities but keeps the energy levels constant.

[@SoumilSahu]

thanks for clearing that up!

[@shivanidubey2317]

atleast use a white background for better view

[@TMPChem]

Strongly disagree. While research suggests that for a single color, black text on a white background is likely superior than vice versa for reading comprehension, I believe the ability to quickly distinguish blocks of text by color is much lower with a white background than a black background. I have had a student send me color-inverted slides they used for printer-friendliness. While fine for grayscale or black and white printing, I like the dark background slides much better on screen.

[@DrJay-wr1df]

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