Develop a kinetic argument to show that in a noninteracting system the average value of the quantity

Question:

Develop a kinetic argument to show that in a noninteracting system the average value of the quantity $\sum_{i} p_{i} \dot{q}_{i}$ is precisely equal to $3 P V$. Hence show that, regardless of relativistic considerations, $P V=N k T$.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Statistical Mechanics

ISBN: 9780123821881

3rd Edition

Authors: Paul D. Beale

See More Books

Question Posted: Mar 16, 2024 07:00 AM

See More Questions

Python and most Python libraries are free to download or use, though many users use Python through a paid service. Paid services help IT organizations manage the risks associated with the use of...
QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...
can someone solve this Modern workstations typically have memory systems that incorporate two or three levels of caching. Explain why they are designed like this. [4 marks] In order to investigate...
What are the advantages and disadvantages of seismic reflection data sets?
When you turn the shaft of an electric motor by hand, what occurs in the interior coils of wire?
A string of mass m is fixed at both ends. The fundamental tone oscillations are excited with circular frequency w and maximum displacement amplitude a max. Find: (a) The maximum kinetic energy of the...
Your instructor will divide your class randomly into groups of four to six people. Acting as a team, with everyone offering ideas and one person serving as official recorder, each group will be...
Chapman Department Store is located in midtown Metropolis. During the past several years, net income has been declining because suburban shopping centers have been attracting business away from city...
The following scenario will be used for the next three questions. Thorin Corp. began operations in 2017. It is a merchandiser of a single item - Product Q and uses the Periodic Inventory method. The...
The energy eigenvalues of an $s$-dimensional harmonic oscillator can be written as \[ \varepsilon_{j}=(j+s / 2) \hbar \omega ; \quad j=0,1,2, \ldots \] Show that the $j$ th energy level has a...
Show that in the relativistic case the equipartition theorem takes the form \[ \left\langle m_{0} u^{2}\left(1-u^{2} / c^{2}ight)^{-1 / 2}ightangle=3 k T \text {, } \] where $m_{0}$ is the rest...
Gerhard News collects payments from customers for newspaper subscriptions on a yearly basis (specifically, in one- year subscriptions). Each month, Gerhard must record an adjusting entry to recognize...
For the beam structure shown below, find all support reactions, draw the Shear Force Diagrams and the Bending Moment Diagrams (assuming El is constant for all members) using the following methods: 1....
By induction prove that Vn E Z+, Problem 2. [25 points] By induction prove that Vn Z+, IM 2 n(n + 1)(2n+1) 6 (3)-3 m Hint: recall from class that i = m(m+1) 2 i=1 Problem 3. [25 points] By...
Compute the projected annual cash flow in Rands. (b) Compute the projected operating gains/losses over the four-year horizon as the discounted present value of change in cash flows, which is due to...
For the following draw the supply and demand for dollars to euros and the reciprocal. Please use real exchange rates for the market equilibrium. Include a short explanation using the correct terms to...
What is the activity that verifies project requirements are technically met? Explain
Two long straight parallel wires are 15cm apart. Wire A carries 2.0 A current. Wire Bs current is 4.0 A in same direction. Determine the magnetic field magnitude due to wire A at the position of wire...
H Corporation has a bond outstanding. It has a coupon rate of 8 percent and a $1000 par value. The bond has 6 years left to maturity but could be called after three years for $1000 plus a call...
Synchronized clocks A and B are at rest in our frame of reference, a distance five light-minutes apart. Clock $\mathrm{C}$ passes $\mathrm{A}$ at speed (12/13) $c$ bound for $\mathrm{B}$,...
A primed frame moves at $V=(3 / 5) c$ relative to an unprimed frame. Just as their origins pass, clocks at the origins of both frames read zero, and a flashbulb explodes at that point. Later, the...
The relativity of simultaneity. Two clocks are placed at rest on the $x^{\prime}$ axis of the primed frame, clock A at $x^{\prime}=0$ and clock B at $x^{\prime}=L_{0}$. They are therefore a...
A set of Christmas tree lights consists of 60 identical bulbs connected in series. When they are connected to a constant 240 V electricity supply, the bulbs dissipate 2.00 W of electrical power each....
The rate capability of a lithium-ion cell is described with the Shepherd equation. Assume that the battery has a capacity of 9A h. An individual cell has an equilibrium voltage of 4.131 V and is...
3. Perturbation Theory. Consider a quantum mechanical particle in a square po- tential well i.e. the 2D 'particle-in-a-box' of length 2a, with Vo(x, y) = 0 for a < x, y < a and V(x, y) = otherwise....

Develop a kinetic argument to show that in a noninteracting system the average value of the quantity

Question:

Step by Step Answer:

For the first part of this problem see S...View the full answer

Statistical Mechanics

Students also viewed these Sciences questions