Recent content by ussername

  1. U

    Euler-Lagrange equation on Lagrangian in generalized coordinates

    How did you come to this equation? I derived Euler-Lagrange with Cartesian coordinates (i.e. ##\vec{r_i}##, ##\vec{v_i}##, as showed in that textbook) but there is no clue it should be valid for generalized coordinates ##q_{\gamma}, \dot{q_{\gamma}}##.
  2. U

    What is the meaning of the bond's yield to maturity?

    And the 6% can be approximately obtained from this expression: $$\cfrac{\cfrac{50+50+50+50+1050-957.35}{5}}{957.35}$$
  3. U

    What is the meaning of the bond's yield to maturity?

    Consider a five-year, 1000 dollars bond with a 5% coupon rate and annual coupons. If this bond is currently trading for a price of 957.35 dollars, what is the bond's yield to maturity? F = 1000 dollars c = 0.05 P = 957.35 dollars N = 5 years y = ? I used the formula presented here for the...
  4. U

    Calculating Diffusion Velocity in Electrochemical System

    I found this problem when I was trying to derive the relation for diffusion time of ion ##i##: $$\tau^{dif} = \frac{d^2}{D}$$ In order to understand what ##\tau^{dif}## really means, it is useful to define ##v^{dif}##. By the way ##v^{dif}## can be measured no worse than for example molar...
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    Calculating Diffusion Velocity in Electrochemical System

    Let's suppose an electrochemical system with given coordinates: We are interested in diffusion motion of ion ##i## in the direction of ##y## axis. Concentration ##c_i## is a function of both ##x## and ##y##. Concentration ##c_i## at ##y=0## is zero. The system is steady thus ##\frac{\partial...
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    I Why is Joule-Thomson effect isenthelpic?

    Let's have an experimental apparatus for realization of Joule-Thomson effect. It could be a thermally isolated pipe with a porous board separating two compartments inside. Different pressures can be set in the second compartment. The gas flows through the pipe and we measure temperature and...
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    I Why is first TD law different for chemical reactors

    My second picture is from the link you posted. I had basically problem to understand where to put enthalpy total differential H=f(T,p,n): $$\frac{\partial H}{\partial \tau}=\dot{H}_{out}-\dot{H}_{in}+\frac{\partial }{\partial \tau}\left (\int_{V}^{ }\frac{\partial H}{\partial m}\,dm \right )$$...
  8. U

    I Why is first TD law different for chemical reactors

    I've learned that first thermodynamic law for some open system is in the form of: where total change of system energy ##\frac{\partial E}{\partial \tau }## is equal to the transferred heat and work. Total change of system energy ##\frac{\partial E}{\partial \tau }## is equal to the energy...
  9. U

    Electrokinetics: charge transfer coefficient

    I'm trying to understand the concept of Butler-Volmer equation and its kinetic derivation. What I don't know and didn't find it anywhere is related to the charge transfer coefficient. Let's have a reaction coordinate during electrode reaction with a transfer of electrons: Can anybody explain...
  10. U

    Pressure dependence of the equilibrium constant for an ideal gas

    You are right, for standard state with ##p^0## it is ##G^0 = f(n_1,n_2,...,n_N) \neq f(p)## and $$\left( \frac{\partial \Delta_{R}G^0}{\partial p} \right)_{T,\vec{n}}=0$$ $$\left( \frac{\partial \ln K}{\partial p} \right)_{T,\vec{n}}=0$$ Just for standard state with ##p## this derivation is not...
  11. U

    Pressure dependence of the equilibrium constant for an ideal gas

    I read in some scripts that equilibrium constant for an ideal gas is not a function of pressure: But that is not generally true! Since: $$\left (\frac{\partial \Delta_{R} G}{\partial p} \right )_{T,\vec{n}}=\Delta_{R} V$$ and $$\Delta_{R} G^{0}=-RT\cdot \ln K$$ it should be: $$\left...
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    Why is the Pumping Power Calculation Resulting in a Negative Value?

    In my view the friction forces within the fluid don't play a role. If I count up work ##dW## done on elements within the pipe, the friction forces of every two adjacent elements are deducted (III. Newton's law). For the whole fluid there remains just a friction force with wall (neglected) and...
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    Why is the Pumping Power Calculation Resulting in a Negative Value?

    If I neglect the friction with pipe wall, I get the shaft work: ##\dot{W}=(p_{in}-p_{out})\cdot A\cdot v=5177000\cdot 0.2\cdot 5=5177000\,W##
  14. U

    Why is the Pumping Power Calculation Resulting in a Negative Value?

    It will be much dissipated heat :) Also the situation with nonzero pressure drop but same temperature on inlet and outlet and adiabatic conditions - it does not make sense (the shaft work cannot be determined from energy balance)?
  15. U

    Why is the Pumping Power Calculation Resulting in a Negative Value?

    It tells us that change of internal energy is nonzero. But how is it possible?
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