Process Definition and 1000 Threads

in this textbook : http://www.fulviofrisone.com/attachments/article/486/Huang,%20Kerson%20-%201987%20-%20Statistical%20Mechanics%202Ed%20(Wiley)(T)(506S).pdf ;page 20 I don't understand about Eq 1.11 come to 1.12 ? I know dU = U_V dT + U_T dV dQ = dU + p dV put dU into dQ. So dQ = U_V dT...

Consider a reversible ideal gas cycle consisting of: 1. An isochoric heat addition, 2. An isothermal expansion to the initial pressure, and 3. An isobaric compression to the initial volume. What, if any, is the difference in net work done by the gas in the cycle if the isochoric heat addition...

I'd be grateful for any formulation that describes this statistical process

I post the working in the attached file

Hello friends, For example; While the carbon ratio in CK45 steel is between 0.42-0.50, the carbon ratio in ST-52 material is 0.22. Is the important factor in the quenching process the carbon content? In here, can we make quenching to CK45 and ST-52? In other words, which types of materials can...

I have already in a previous task shown that A is not irreducible and not regular, which I think is correct. I don't know if I can use that fact here in some way. I guess one way of solving this problem could be to find all eigenvalues, eigenvectors and diagonalize but that is a lot of work and...

Suppose that W(t) is just a Wiener process (i.e. a Gaussian in general). I want to know what the probability density for x, P(x), is. I started off by just assuming that I want to measure the expectation value of an observable f(x), so ##<f(x)>=\int_{W=0}^{W=t}{P(W)f(g(W))dW} \ \ ,\ \ x=g(W) ##...

She is not ready yet to understand the commonly-used example in the field of finance. I don't want to use the growth of a tree's trunk because the process is too slow. I have also told her the 'chess board and rice grain story', but in that story the growth rate is very fast, so doesn't have...

Hi everybody, Academic papers in mechanical engineering use often lumped-element (or lumped-parameter) models such as a typical quarter car model. However, books about the (mechanical) engineering design methodologies (such as by authors Dieter, Shigley, or Pahl-Beitz) seem to not mention this...

For part 1. I need to find the temperature, I rearranged the equation so that: T = pV/nR (28000000)(0.45) / (28.96)(8.314) This gives me a value of 52331.4 I am unsure where the units I have used in the equation are correct. I have used pa for pressure, or should I be using kpa? this would...

Could I have help with what formulas or method that is required in order to solve the problem?

I realize that nothing causes an excited atom to emit a photon, and that it's a random process. But someone was asking me about why energized systems in general tend to lose their energy to the environment and move toward equilibrium. I mentioned that an inflated balloon, given a hole, will tend...

I recently came across this concerning a T-S diagram: https://learnthermo.com/T1-tutorial/ch07/lesson-C/pg04.php The author states that the area under the curve represents the heat transferred reversibly. The author didn't state what actual process the curve represents, but I couldn't think of...

We need to find the system's entropy variation. I don't think i understood pretty well what is happening in this process, can someone help me how to start?

How does the process of collaboration in math work ? Do mathematicians like to share their problems ? Can I do this by e-mail ? How to ask mathematicians if they want to collaborate in a math project ? I'm still learning more advanced math but these are questions I had in mind and didn't know...

So the standard explanation for star formation says we have a disk of gas collapsing into itself until a certain pressure/temperature is reached at which point the star "ignites" and pushes away the rest of the material in the disk. My thinking is, surely this pressure/temperature needed for...

I am trying to find the derivative of this problem using the four step process but keep getting stuck when it comes to the third step of f(x+h) - f(x). I do not know what to do once I reach that step. Am I canceling terms out incorrectly? How should I deal with a fraction over a fraction? Any...

The attempt at a solution follows as an attachment. If you are only interested in the solution without the derivation, look at page 1 and page 9.

i want to known whether virtual particle exist or not , and does exchange of particle really happen in interaction.

I am still new to the theory of relativity (both SR and GR), but I've read few books which gave me an insight about the subject (not a mathematical insight though). There's a question that I really would like to know the answer of: Is there a time delay for the bending of spacetime to occur...

I need help solving this please. Its a past exam paper. requires wort to undergo 5% by mass evaporation in one hour does this mean starting vol is 500hl and after one hour vol should be 475hl Wort volume = 500 hl = 50,000 L / hr 1 L = 10^-3 m^3 50,000 L = 50 m^3 /hr = 0.833 m^3 / min = 0.01388...

Dear experts, Considering a cylinder and a piston where the volume is V and the pressure is P and the temperature being T, the gas is slowly allowed to expand accepting heat keeping the temperature constant at T to twice the volume. The pressure according to the ideal gas equation should go...

MY CONFUSION (WHICH IS WHAT THIS POST IS ABOUT): * The reason why c is not the correct answer is because unitasking just means a system that has one simulatenous user, right? In other words, a unitasking system can still be a multiprogramming system, such that one simultaneous user has the...

I'm not sure that this is an adiabatic process. As far as i can read, it is adiabatic if no HEAT or ENERGY is added. But pumping in molecules that are a non-zero temperature is an addition of energy, no? Anyway - my solution with the assumption of an adiabatic process. (skipping units for...

I tried this question and this the answer given in the book. A cylinder is close at both ends and has insulating walls. It is divided into two compartments by a perfectly insulating partition that is perpendicular to the axis of the cylinder. Each compartment contains 1.00 mol of oxygen, which...

Since the assignment asks the work done by the gas, that should be equal to P1*(V2-V1) aka the area under the P1 line. Do I have to subtract the work done to the system or is this the solution already? If so, why do I need P2?

P1 = 2 bar V1 = 5.1L P2= 1bar V2 = V1P1/P2 = 10,2L, so the volume of gas would double? or should the absolute pressure be taken into account P1= 2bar (3bar absolute), V1=5.1L P2= 1 bar V2 = 15,3L?

The specific example I'm going to give is from a discussion I am having elsewhere, but the question itself, as given in the thread title and summary, is a general one. We have two couples, each of which has seven children that, in order, are six boys and one girl (i.e., the girl is the youngest...

Summary: Derive the formula of power spectrum from Discrete Fourier Transform. Hi all I don't know where should I post this, so if I am wrong, I apologize.(But this is almost math problem so ) I would like to know the calculation process when derive Eq(6.3) in this paper. Eq 2.4a is...

How is to possible to change the temperature without exchange of heat? Could you please give me an example? I know it is possible to keep the temperature constant while there is exchange of heat. This is possible when the heat supplied is consumed/lost to the surrounding. But how is it...

I can get the P2 from P1V1=P2V2 --> P2 = 10Bar, but then how do i get the density? p=p/R*T ? where p=10Bar R=287J K-1kg and T 288K, density would be 12,1kg/m3? Is that right?

I'll admit I am very new to Gaussian processes, but from what I know a Gaussian process is completely determined by a mean vector E(Y(θ)) and a covariance function Cov[Y(θ1), Y(θ2)]. E(Y(θ)) is given, and we have the correlation, which is just the covariance divided by Var(θ1)*Var(θ2).The...

I have defined all the list of components necessary for this process and the chosen property method was (ENRTL-SR). I chose Gibbs reactor to simulate the low-temperature reactor, high-temperature reactor, and chemical absorber because the kinetics of the reactions is not known. Also, the Rstoic...

Assume that an individual only has two possible states: susceptible (S) and infected (I). Further, assume that the individuals in the population are independent, and that for each susceptible individual the time until the next infection follows an exponential distribution with expected value 1/λ...

Consider two Bernoulli processes X1 and X2 such that X1[k] is a Bernoulli random variable with P=0.5 and X2[k] is a Bernoulli random variable with P=0.7 for all k>=0 Let Y be a random process formed by merging X1 and X2, i.e. Y[k] =1 if and only if X1[k] = X2[k] = 1 and Y[k] = 0 otherwise. a.)...

Homework Statement: A PV diagram shows an isobaric expansion, I'm asked to know the signs of: work done on, heat added to, and change in energy content of the system. Homework Equations: W= integral (P dV), dU = Q + W Since this is an expansion, the system does work on the surrounding and...

Hello forumites, I've been working with the following expression for the change in internal energy in an isentropic scenario. $$dU = n*c_v *dT = -pdV$$ However, I'm a bit stumped here, the left hand side of the expression (or middle rather), states the change in internal energy is the...

Why is a thermally isolated process that occurs sufficiently slow is necessarily adiabatic and not just reversible process ? Here I mean that the definition of adiabatic process is no change in the entropy of the subsystem, and a reversible process is define by no change of the total entropy of...

Hello everybody! I have to write the Feynman diagrams for the process ##\pi^- + p \rightarrow \Lambda_c^+ + D^-##. It is a strong process since all the quantum numbers are conserved. I have attached my attempt, is it correct? Thank you all in advance!

You knew there is a cutting force in the orthogonal process, it is exerted by cutting speed, buy why have a feed force?

*Here, no mention of these reservoirs being a gas, so I'm not sure if I can use the PV=nRT or the P*V^(gamma)=K equation. SO I am left with only the 1st law. If I can write dQ1( going out from object 1)= Cp (indep of T)*(Tf-T1) dQ2(coming into the object 2)= Cp*(T2-Tf)...

I am self studying thermodynamics and I stumbled upon the concept of a quasi-equilibrium process which I don't fully understand but here are my thoughts, Equilibrium is a condition of balance characterized by the absence of driving potentials and at such conditions you can measure properties...

Apologies if this has been discussed elsewhere. I know a Poisson process implies a Poisson distribution, but does a Poisson distribution imply a Poisson process? and does the absence of a Poisson distribution imply the absence of a Poisson process? TIA - Sunil

Now, ## \displaystyle dQ=\left(\frac{\partial Q}{\partial p}\right)_V dp+\left(\frac{\partial Q}{\partial V}\right)_p dV## In an adiabatic change, ##dQ=0##. So, ## \displaystyle\left(\frac{\partial Q}{\partial p}\right)_V dp+\left(\frac{\partial Q}{\partial V}\right)_p dV=0## Using (3) and...

Hey! :o We consider the equation \begin{equation*}u_{k+1}=\begin{pmatrix}a & b \\ 1-a & 1-b\end{pmatrix}u_k \ \text{ with } \ u_0=\begin{pmatrix}1 \\1 \end{pmatrix}\end{equation*} For which values of $a$ and $b$ is the above equation a Markov process? Calculate $u_k$ as a function of $a,b$...

A Galton Watson branching process B is defined P0 = 1/3 ; P1 = (1 - c)2/3 and P2 =c 2/3 where pi is the probability to have 'i' offsprings (C in [0,1]). a) compute the critical value C* such that for C<= C* the prcesss B will die out with probability one and for C > C* the process will...

The refrigeration process is used in air conditioning to dehumidify and control temperatures in homes and buildings. The heating industry preceded the air conditioning business and many evaporator coils were placed on top of furnaces to create split systems and utilize existing ductwork. The...

Hi, I was doing this question and I was slightly confused as to whether I ought to just substitute n = \gamma (the adiabatic constant) into the equation? The answers don't do this, but I was wondering why it was wrong for me to do so? This was only a small fraction of the question (which was...

If I am honest with you I don't even know where to start, if someone wouldn't mind helping me find a starting point? Additional information Melting point of aluminium 660°C Specific heat capacity for aluminium (cp): 0.91 kJ/kgK...