# Search results

1. ### Complex circuit and its resistance

The true answer is : The voltage between P and Q is 1.5 V. I got stuck finding the total resistance. My question is: Is B parallel to both A and C? Is C parallel to D ? I tried many ways to find the total R but failed! My first attempt: I say the system ABD is in serie with C...
2. ### Which lamp is dimmed in the circuit?

The true answer is B. But I dont understand why! I know: Kirchhoff's circuit laws : ∑In=0 If we assume that a current that goes from plus to minus, before it passes through lamp B, I know that according to Kirchhof's laws, part of the current will pass through the bottom path where there is no...
3. ### Clausius' theorem

I see this in my book but there is something I don't get! If we consider a Carnot cycle where heat Qh enters and heat Ql leaves, We know Qh/Ql=Th/Tl And we define ΔQ_rev then : ∑(ΔQ_rev/T) = (Qh/Th) - (Ql/Tl) =0 I insert an image: Which shows the heat dQi entering the reservoir at Ti from a...
4. ### Change in Entropy for an isolated system

ΔU_A + ΔU_B = 0 (Is this because of isolated system am I right?) ΔU_A = CA * (T_final - T_A ) ΔU_B=CB * (T_final-T_B) And because of a very slow process : S=ln(T) T_final= (CA T_A + CB T_B)/(CA + CB) ΔS_final = CA*ln(T_f/TA) + ln(T_f/TB) * CB My QUESTION is : When we say No heat exchange...
5. ### Useful work and an ideal gas

What do I see in my solution is : ΔW + ΔQ = W_pv + W' + ΔQ (A little difficult to perceive the useful work ) Work on the environment : -p0*(-ΔV) (WHY negative sign?, Is this the work ON the gas?) ΔV=nR (T0/p0 -T/p) By TdS = dQ ΔS + ΔS0 =0 Reversible case: ΔU= -T0ΔS - (-p0(-ΔV)) + W' (WHY...
6. ### Reversible heat engine

My attempt: I though : ΔQ_w= 1*4200 * (-100) J=-420000J Q_ice=334000*m_ice = ΔQ_w But it was totaly wrong! The solution showed : Because the heat engine is reversible the efficiency η = 1- (T_cold / T) T_cold is always 273 K while the hot temperature changes from 373 K to 273 K during this...
7. ### Eigenvector of raising operator

Homework Statement show that the raising operator at has no right eigenvectors Homework Equations We know at|n> = √(n+1)|n+1> The Attempt at a Solution we define a vector |Ψ> = ∑cn|n> (for n=0 to ∞) at|Ψ>=at∑cn|n>=∑cn(√n+1)|n+1> But further I give up!:cry:
8. ### Finding state vectors for pure states!

Homework Statement Is the following matrix a state operator ? and if it is a state operator is it a pure state ? and if it is so then find the state vectors for the pure state. If you dont see image here is the matrix which is 2X2 in matlab code: [9/25 12/25; 12/25 16/25] Homework...
9. ### Probability theory and statistics

Homework Statement The time (minute) that it takes for a terrain runner to get around a runway is a random variable X with the tightness function fX = (125-x)/450 , 95≤x≤125 How big is the probability of eight different runners, whose times are independent after 100 minutes: a) Everyone has...
10. ### A paradox in probability theory and statistics

Homework Statement In a vessel is a 5 cent coin and two 1-cent coins. If someone takes up two randomly chosen of these coins, and we let X be the total value of the coins taken, what is the probability function for X? Homework Equations I know that X has a value {2,6} The Attempt at a...
11. ### Force of magnetic attraction between hemispheres

Homework Statement Calculate the force of magnetic attraction between the northern and southern hemispheres of a uniformly charged spinning spherical shell, with radius R, angular velocity ω and surface charge density σ. Homework Equations Maxwell Tensor : Tm = [/B](1/μ) * ((B*n)B -...
12. ### Potential of a circle boat

Homework Statement A line charge has the total charge Q evenly distributed over a circle boat with radius a and sector 2β, placed according to the figure Find the Electric field E and the potential V in the origin. Homework Equations I know for this case that E(r) = (1/4πε) ∫ (λ(r')/R2)R...
13. ### Energy and Compton scattering

Homework Statement Compton scattering can be used both to measure the direction and energy of photons in nuclear physics experiments. For a particular preparation a spectrum of Compton scattered electrons was measured which clearly corresponded to a generally monochromatic gamma radiation. The...
14. ### Plotting with Matlab

Homework Statement I have a function : and I want to draw : Homework Equations where T has values : 600, 800, 1000, 1100 And λ:(0,10*^-5] I have to use max function with two values and the solution must not consist of repeating four times of similar snippets of code, one for each curve.The...
15. ### Length contraction & muons

Homework Statement A muon is created in the atmosphere 3 km above Earth's surface, heading downward at speed 0.98c. It survives 2.2 * 10-6s in its own frame of reference before decaying. Relativistitically, according to the muon, what is the distance from the point in the atmosphere where the...
16. ### Direction of friction

Homework Statement A homogeneous semicircular disc of mass m and the radius r is released from rest in the vertical position shown in the figure. Determine a minimum value of the coefficient of friction μ between the disc and the horizontal surface that prevents sliding in the initial moment...
17. ### Fourier series and differential equations

Homework Statement Find the values of the constant a for which the problem y''(t)+ay(t)=y(t+π), t∈ℝ, has a solution with period 2π which is not identically zero. Also determine all such solutions Homework Equations With help of Fourier series I know that : Cn(y''(t))= -n2*Cn(y(t)) Cn(y(t+π)) =...
18. ### Finding inverse of a Laplace transform by convolution

Homework Statement find the inverse Laplace transform of the given function by using the convolution theorem Homework Equations F(s) = s/((s+1)(s2)+4) The theorem : Lap{(f*g)(t)} = F(s)*G(s) The Attempt at a Solution I know how to find it the answer is : we have 1/(s+1) * s/(s+4) and the...
19. ### Laplace Transform of this function

Homework Statement We want to find the Laplace transform for f(t): 0 for t≤2 and (t-2)2 for t≥2 Homework Equations I know that Lap{uc f(t-c)} = e-csLap{f(t)}=e-csF(s) I rewrite f(t)=0+g(t) where g(t) = 0 for 0≤t<2 and (t-2)2 for t≥2 so we can write f(t)=g(t)= u2(t)*(t-2)2...
20. ### Laurent series

Homework Statement Expand the function f(z)=1/z(z-2) in a Laurent series valid for the annual region 0<|z-3|<1 Homework Equations I know 1/z(z+1) = 0.5(1/(z-2)) - 0.5(1/z) Taylor for 0.5(1/(z-2)) is : ∑(((-1)k/2) * (z-3)k) (k is from 0 to ∞) For the second 0.5(1/z) the answer is a...
21. ### Real part of a analytic function

Homework Statement Show that xux + yuy is the real part of an analytic function if u(x,y) is. To which analytic function is the real part of u = Re (f(z))? Homework Equations What I know about analytic functions is Cauchy-Riemann condition (∂u/∂x) =(∂v/∂y) and (∂y/∂y)=-(∂v/∂x) I know...
22. ### Differential equations and geometric series

Homework Statement I Have a differential equation y'' -xy'-y=0 and I must solve it by means of a power series and find the general term. I actually solved the most of it but I have problem to decide it in term of a ∑ notation! Homework Equations y'' -xy'-y=0 The Attempt at a Solution I know...
23. ### Finding derivative of Z^(7/3)

Consider the principal branch of the function f(z)= z7/3 Find f'(-i) and write it in the form a+bi My attemp is : I know zc = exp(c logz) and the derivative of that is : (c/z) * exp(c Logz) That is in this case (7/3)*(i) *exp((7/3)*Log-i) = f'(-i) I know that Log(-i) = Log(1) + i(-pi/2)= -i...
24. ### Work and Carnot process

Homework Statement An ideal Carnot process operates between a heating bath with the temperature of 20 C and a mole of hydrogen is in a container with constant volume. During the process, the work is done to remove heat from the hydrogen gas and emit heat to the heat bath. Calculate the work...
25. ### Linear Algebra and polynomial

Homework Statement Let T: P2 --> P3 be the transformation that maps a polynomial p(t) into the polynomial (t+5)p(t). a) find the image of p(t)= 2-t+(t^2) b) Find the matrix for T relative to bases {1,t,t^2} and {1,t,t^2,t^3}. Homework Equations Given The Attempt at a Solution a) I know...
26. ### Change of entropy

Homework Statement to illustrate an aspect of the second law of thermodynamics, we regard entropy changes in two cases. We have a vessel with 1 kg of warm water with T = 80 C and another vessel with 2 kg of cold water with T = 10 C and we mix them. Case 1: we pour hot water in the vessel with...
27. ### Using heat pump to make a house heater

A heat pump in winter heat energy from the bottom of a lake, where temperature is 4 ° C and delivers thermal energy in a home where the temperature is 22 C. What is the theoretical minimum power the heat pump must be supplied to you at home must be able to take out 4000 watts heating power ...
28. ### Change in entropy

1 kg of iron with the temperature of 323 K to 293 K is cooled by dipping into a large water bath temperature of 293 K. What is the total entropy change? Relevant equations dS = mcdT/T S=mc *ln(T2/T1) C iron = 450J/(kgK) C water= 4200 J/(kgK) m water = I see in my book 1 kg in solution The...
29. ### Value of gamma in adiabatic process

In conjunction with diving, a mixture of helium and oxygen called heliox. It will form the background to the following model invoice. Suppose that 1 mole of He and 1 mole of O2 is compressed as fast at half the volume that no heat exchange with the environment have time to take place...
30. ### Effusion and isotopic composition

1. In a gas UF6 (uranium hexafluoride) are uranium atoms of both the fissionable uranium isotope 235U , and 238U. To enrich the fissile isotope can let a gas UF6 with natural isotopic composition (0.7% 235U, 99.3% 238U) undergo effusion process. The process is then repeated in many steps in the...