Making use of the fact that the entropy S(N, V, E) of a thermodynamic system is an extensi quantity, show that as as as N (³5) + V (#5) N.F + E(³E) N.V (AN), av V,E N,E N, Note that this result implies that (-Nu + PV + E)/T = S, that is, Nμ = E + PV - TS. = S.
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- For a p, v, T system formed by a mole, it has been empirically obtained that the internal energy per unit mass can be written in the form: u = apv+b, where a, b are constants. Find the equation for the adiabat in this system.A plastic bag containing 0.2 kg of water at 20°C is dropped from a height of 0.5 m onto an insulating carpet. Assume that the bag does NOT break. What is the approximate probability that a similar bag sitting on a carpet will do the reverse; that is, spontaneously jump 0.5 m in the air? Express your answer in the form "Probability = 10-x," where x is a number you will calculate. (Hint: Note that ey = 10y÷ln(10).)Problem 3: Starting with the expression derived in the lecture notes for the multiplicity of an ideal 1 n3N/2 (2m)³N/2 N! (3N/2)! h3N gas VNU3N/2 derive the Sackur-Tetrode expression for the entropy.
- The natural variables for the internal energy U are the entropy S and the volume V. This means that, if you know S and V, you can find U(S, V) and simple expressions for T and P. Supposed instead that you know U(T, V). Show that this leads to the following expression for P: -/), dT + f(V) T aV T2 where f(V) is an arbitrary function of V.Answer in 90 minutes please.zemansky thermodynamics book
- For a dilute gas of N monatomic particles with mass m and total energy E, use the Sackur- Tetrode equation for the entropy S V = log + NkB to derive expressions for the pressure and internal energy in terms of the temperature T and volume V. [You may use that X₁ = 3πh² N/(mE).] thPolymers, like rubber, are made of very long molecules, usually tangled up in a configuration that has lots of entropy. As a very crude model of a rubber band, consider a chain of N links, each of length L Imagine that each link has only two possible states, pointing either left or right. The total length L of the rubber band is the net displacement from the beginning of the first link to the end of the last link. Using the thermodynamic identity, you can now express the tension force F in terms of a partial derivative of the entropy. From this expression, compute the tension in terms of L, T , N, and l.