Answered: Consider a system of N free particles… | bartleby

Related questions

Question

Consider a system of N free particles in which the energy of each particle can assume
two and only two distinct values, 0 and E (E > 0). Denote by nɔ and n the occupation
numbers of the energy level 0 and E, respectively. The total energy of the system is U.
(a) Find the entropy of such a system.
(b) Find the most probable values of no and n¡, and find the mean square fluctuations of

Expert Solution

Trending now

This is a popular solution!

Step by step

Solved in 3 steps

SEE SOLUTION Check out a sample Q&A here

Blurred answer

Similar questions

A 23.9 g block of copper whose temperature is 382 K is placed in an insulating box with a 57.3 g block of lead whose temperature is 228 K. (a) What is the equilibrium temperature of the two-block system? (b) What is the change in the internal energy of the two-block system between the initial state and the equilibrium state? (c) What is the change in the entropy of the two-block system? The heat capacities of copper and lead are 386 J/kg-K and 128 J/kg-K, respectively. (a) Number i (b) Number i (c) Number i Units Units Units
Please help me
When a metal bar is temporarily connected between a hot reservoir at Th and a cold reservoir at Tc, the energy transferred by heat from the hot reservoir to the cold reservoir is Qh. In this irreversible process, find expressions for the change in entropy of the following. (Use any variable or symbol stated above as necessary.) (a) the hot reservoir ΔSh = (b) the cold reservoir ΔSc = (c) the Universe ΔSU =
One of the statements of the second law is that “heat cannot flow from a colder body to awarmer one without external aid”. Assume two systems, 1 and 2, at T1 and T2 (whereT2 > T1 ). Show that if a quantity of heat q did flow spontaneously from 1 to 2, the processwould result in a decrease in the entropy of the universe. [You may assume that the heat flowsso slowly that the process can be regarded as reversible. Assume also that the loss of heat bythe system 1 and the gain of heat by 2 do not affect T1 and T2 .]
(a) What is the unit of "specific entropy"? Is it an extensive property? (b) What is an isentropic process? Please give an example. (c) Explain the increase of entropy principle. (d) The entropy of a hot baked pizza decreases as it cools. Is this a violation of the increase of entropy principle? Explain.
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).] th
Polymers, 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.
A box contains 100 gas molecules all released on the left side of the box. What is the initial entropy of all the gas molecules on one side? You can calculate the number of microstates (left/right distribution of molecules) possible by the equation W = N! / ( nL! * nR!,) where N is the total number of molecules and nL is the number on the left and nR is the number on the right. What is the entropy of the most disorganized distribution of gas molecules?
A rigid box contains 0.9 mol of an ideal monoatomic gas. Heat is added to the gas and its temperature changes from 183 K to 295 K. If this is a reversible process, what is the change in entropy of the gas in J/K?