What is Process: Definition and 1000 Discussions

Homework Statement Assume that a gas obeys the VDW Virial expansion Pv = RT + (b-a/RT)P to first order in P and u = 3RT - aP/RT to first order in P, where v and u are molar quantities. In the following cycle (see attachment), the heat transferred to the gas is transferred by direct thermal...

Homework Statement Let X(t) and Y(t) be independent Poisson processes, both with rates. Define Z(t)=X(t)+Y(t). Find E[X(1)|Z(2)=2]. 2. The attempt at a solution...

Homework Statement Explain whether or not the first or second law of thermodynamics are violated in the below cyclic process (see attachment) Homework Equations Clausius Inequality, Carnot efficiencies, ΔS ≥ 0 for a cyclic process. The Attempt at a Solution The first law is...

Homework Statement A Wiener Process W(t) is a stochastic process with: W(0) = 0 Trajectories almost surely continuous Independent increases, that means, for all t1 ≤ t2 ≤ t3 ≤ t4, we have (W(t2) - W(t1)) is independent of (W(t4) - W(t3)) For t ≤ s, (W(s) - W(t)) follows a normal centered...

Homework Statement A nearly flat bicycle tire becomes noticeably warmer after it has been pumped up. Approximate this process as a reversible adiabatic compression. Assume the initial pressure and temperature of the air before it is put in the tire to be Pi = 1.00 bar and Tf 287K . The final...

Hi, I have a general question about polytropic processes when working with an ideal gas. A polytropic process is one for which PV\gamma = constant. What I am wondering is if we assume that n is constant, does that mean that the temperature does not change for the process? I see that...

term “scattering” more of a general process Is the term “scattering” more of a general process which incorporates the linear effects of reflection, refraction and diffraction?

Homework Statement Given X(t) = cos(2\pi50t + ω), where the stochastic variable ω is uniformly distributed between 0 and 2\pi. Suppose the sampling frequency fs is 30 Hz. What frequency interval is covered after the sampling? Homework Equations Normalized frequency when sampling can be...

I can't seem to model this properly. This isn't an assignment, I'm just curious how this will go, lol. So I have this tank with an incoming feed stream with temperature Ti, and an output stream T. It has a jacket where q would be modified depending on the desired output stream T. So I...

In an isobaric process of 1 mole of a monatomic ideal gas, the pressure stays the same while the volume and temperature change. Let's take an isobaric expansion where the volume increases by 2m3 and the pressure stays at 5kPa. If the work done by the gas is the pressure times the change in...

I am posting here because this is NOT homework. Problems are finished. However we have an exam on friday for calculus 1 class and well... I've been trying real hard to understand it but professor has a real strong accent and he speaks too low, no one can hear a thing! Anyway, we did the...

Homework Statement Consider a discrete time birth and death process in which the maximal population size is N = 6. Birth rates and death rates are directly proportional to the current size Xt of the population at time t (t = 0; 1; 2; : : :). If the maximal population size is reached, no more...

Homework Statement The angular velocity of a process control motor is (21−(1/2t^2)) rad/s, where t is in seconds. 1.) At what time does the motor reverse direction? 2.) Through what angle does the motor turn between t =0 s and the instant at which it reverses direction? Homework Equations...

Homework Statement Let {W(t); t >= 0} be a Wiener process. Determine the auto-covariance function for the process {X(t); t >= 0} defined by X(t) = e^(-ct) * W(e^(2ct)) for all t >= 0, where c > 0 is a constant. Is {X(t); t >= 0} stationary in the wide sense? Homework Equations Is...

Homework Statement Let ##v_{1},...,v_{m}## be an orthonormal set of vectors in ##V##. Let ##v\not\in S(v_{1},...,v_{m})##. Show that the vector ##v'=v-\sum\limits_{i=1}^{n}(v,v_{i})v_{i}## given by the Gram-Schmidt process has the shortest length among all vectors of the form ##v-x## for ##x\in...

In work that I've been doing, we've come across an interesting problem. In a manufacturing process, a highly viscous, non-Newtonian fluid goes down a vertical chute and then gets pushed horizontally out the bottom by some rotating screws. Sometimes, the fluid gets pushed out the bottom, but...

In Bayer's process in the digester both water soluble sodium aluminate and sodium silicate are formed. After that my textbook says cooling the sodium aluminate it crystallizes to to give aluminium hydroxide and sodium hydroxide. My two questions are, one, in the digester alumina reacts with...

Arrivals are Poisson distributed with parameter \lambda. Consider a system, where at the time of arrival of a tagged packet, it sees N_Q packets. Given that the tagged packet arrives at an instant t, which is uniform in [0, T], what is the probability that all N_Q packets arrived in [0,t]?This...

The low is: dQ=dU+p dV but the specific heat to volumen (in a perfect gas) cte is: C_v = \frac{dQ}{dT} = \frac{dU}{dT} why if in adiabatic proces dQ=0, then C_v \neq 0 ?? http://en.wikipedia.org/wiki/Adiabatic_process#Ideal_gas_.28reversible_process.29

Hi, I'm trying to solve the following question, but unsure how to approach it. A paper manufacturing process states (in its specifications) that each piece of paper's weight will be less than the nomial weight of 1.2 grams on NO MORE than 1 occasion in 100. Currently, the process produces to...

In an adiabatic process PVγ=constant Now I thought the work done by an ideal gas in an adiabatic process was given by the equation here: http://hyperphysics.phy-astr.gsu.edu/hbase/thermo/adiab.html But while doing a GRE question the answer was given as PfVf - PiVi / 1 - γ Is this...

Why can't the Sun (or any star) fuse elements higher than iron? Could anyone provide a technical answer? Thanks!

I had a problem that said "I throw nine balls randomly in five containers. What's the probability any container will have exactly five balls by the end of the process?" The answer involved using a Binomial distribution. Now the question is, how do I train my mind to go to the use of...

Homework Statement One mole of ideal gas expands from an initial volume V1,to a final volume V2. Where V1 and P1 correspond to the volume and initial gas pressure, whereas V2 and P2 correspond to the volume and pressure at the end of the process. The process is described by the equation...

Apologies if this has been asked before but I couldn't find any posts with the exact question. I'm about to go to college but I haven't decided my major yet. I have loved physics, particularly astronomy, ever since I was a child. I used to read a lot of astronomy books when I was younger...

Homework Statement An ideal gas undergoes the following reversible cycle: (a) an isobaric expansion from (P1, V1) to (P1, V2), (b) an isochoric reduction from (P1, V2) to (P2, V2) (c) an isobaric reduction from (P2, V2) tp (P2, V1) (d) an isochoric expansion from (P2,V1) to (P1, V1). What...

Homework Statement So I keep evaluating these limits wrong. Something is wrong in my thought process. Homework Equations http://www.calcchat.com/book/Calculus-ETF-5e/ chapter 9, section 1, question 69 Consider A_n = (1+k/n)^n If I wanted to see if it converged or not I would just...

My university is offering a course called "Stochastic Process". The only prerequisites to this course according to my university is a course in Probability which uses the book by Rosen. I've read elsewhere that the course actually requires more of analysis (functional analysis and measure...

Does anyone have any idea why the process epsilon meson to eta meson is forbidden? bb' --> cc' Mass Energies 9.3 GeV --> 3.0 GeV The solution set simply says that this is kinematically forbidden. It seems to me that in the center of momentum frame the products can have whatever...

How would you take the Ito integral of an arbitrary f(W_T) where W_T is a standard Wiener process X_T=\int^t_0 f(W_s)dW_s would you somehow use Ito's lemma? I have attempted, but it doesn't seem to make sense... dX_T=f(W_T)dW_T, There doesn't seem to be a f(x) that makes sense for this in...

My goal is to build a software program that simulates the function of the eye. As I (barely) understand things, a single photon can bounce off an object and enter my eye. Q1 - Does the photon determine the color? If not, what determines the color of that single wave/particle? Q2 - How...

Hello everyone, I'm doing some practice problems for my final exam. I came across this question: «The Haber process is being used at a pressure of 76 000 mmHg at a temperature of 450°C. Gaseous ammonia is cooled and collected after its production, in order that its temperature does not...

Is additive color mixing a linear process (or close to)? (if this question has already been answered in detail, please forward me) If the answer to this question is "yes" then: Considering three hypothetical LEDs: Red T-1 (650nm λ), 60° viewing angle, 1000mcd luminous intensity...

Hello can someone please give me an example of TWO industrial process which uses and depends on gas pressure or the change in gas pressure. Basically did this but instead wrote about gas Laws uses in different things so have to re do it (didn't read the question as we were learning about gas...

Hi can please check my answer for this question : A certain Gas of volume 0.4 m3, pressure of 4.5 bar and temperature of 1300 C is heated to in a cylinder to 9 bar when the volume remains constant. Calculate ¨ (i) Temperature at the end of the process, ¨ (ii) the heat...

Homework Statement Here's a quick sketch of the problem: http://prntscr.com/15ltr5 Essentially, Sugar Solution enters the first evaporator at 65°C and the water is boiled (to 100°C) so that a sugar concentrate comes out (bottom of evaporator) and saturated steam leaves the evaporator...

Hello Can we consider the sentence “Adiabatic process cannot decrease entropy” (found for example here) to be true in any circumstances ? Here I do not want to focus on any particular situation. Hence the system is not necessarily a (perfect) gas; the transformation is not necessarily...

Homework Statement Two 100g Aluminum cubes with T1 = 80° C and T2 = 20°C Specific heat of Al is .22 cal/g/°C. The cubes are placed in contact and in short period of time a quantity of heat, dQ , is transferred from T1 cube to T2 cube. The cubes temperatures now are 75°C and 25°C. After a...

For an irreversible process: S2 - S1 > ∫12 dQ/T In the case of heat transfer dQ between object with T1 to object with T2, T1 > T2 ΔS in Joules/K is known But for evaluating ∫12 dQ/T = ln dQ/T - ln dQ/T . d/Q is known but what values for T in this case ? Object 1 & 2 have Temperatures before...

Homework Statement (see attachment, ignore the arrows made with the pen) Homework Equations The Attempt at a Solution Efficiency of a cycle is defined as ##\eta=\frac{W}{Q}## where W is work done and Q is heat input. W can be easily calculated by finding the area enclosed...

Problem statement: Define the random process X(t) = C where C is uniform over [-5,5]. a) Sketch a few sample realizations I need reassurance that if I do a a few sample realizations of this random process they are all going to look the same. They are going to be an horizontal line with...

Hello, I've always had problems conceptualizing the physics behind circuits, and it always felt like information is hidden from me. Lately I've been trying to analyze circuits in the microscopic and electrostatic way, as i think it is crucial for real understanding of circuit concepts. I've...

Hi does anyone know the "formula/process" for the least square method if the are giving several (x,y) points and asking me to find y=Ax^2 + B?

Hello all, I have the following continuous-time random process: v(t)=\sum_{k=0}^{K-1}\alpha_k(t)d_k+w(t) where d_k are i.i.d. random variables with zero mean and variance 1, alpha_k(t) is given, and w(t) is additive white Gaussian process of zero-mean and variance N_0. Can we say...

Hi There, quite an informative forum.Im struggling with a question which reads as follows: At a certain point during the expansion cycle in a steam engine cylinder, the steam pressure was 1.1 MPa and the dryness 0.85, At the end of the expansion process the pressure was 0.28Mpa and the dryness...

attached is an example question i am working through, i would appreciate if anybody could explain to me the part in the red box. I understand the relationship linear acceleration = ang acceleration*radius however, this working appears to divide the angular equation by the radius? thanks

Homework Statement Use the Laplace transform approach to find the renewal function for a renewal process with interrenewal p.d.f. as follows: g(x) = (c^2)xe^(-cx) , x > 0 The Attempt at a Solution M*(s) = G*(s)/(1-G*(s)) where M*(s) and G*(s) denote laplace transforms I have that G*(s) =...

Homework Statement Homework Equations Zero-momentum frame is defined as the frame in which total momentum is zero. The Attempt at a Solution (a) In terms of the zero momentum variables, (e1 and e1 are to distinguish the two resultant particles) \vec{p'}_{HE} +...