Prove that the adiabatic process of an ideal gas in a
simple compressible closed system is the polytropic process of n=k
( where k is the specific heat rate) by using the thermodynamic
first law.
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a statement of the first law of thermodynamics is that a. in a
spontaneous process, the entropy of the universe increases b. there
is no disorder in a perfect crystal at 0 k. c. the total energy of
the universe is constant. d. the totla energy of the universe is
constant. e. mass and energy are conserved in all chemical
reactions
Describe evidence that supports boyles law, PV = constant for an
isothermal process. describe difficulties for exploring this
law
Describe evidence that supports gay-lussac's law, p/t = constant
for an isovolumeteric process. describe difficulties exploring this
law
Describe evidence that supoorts charle's law, v/t=constant for an
isobaric process. describe difficulties exploring this law
(a)Use Netwons Second Law of Motion to prove that the equation
governing the forced damped harmonic oscillator (spring-mass
system) is: mx"(t) + cx'(t) + kx(t) = F(t): (Explain what the
constants m; c; k are and what the function F(t) is. Draw a picture
of the system.)
(b)Assume m = 1; c = 0; k = 4; that F(t) = cos(2t); and that the
object attached to the spring begins from the rest position. Find
the position function using the...
State and prove the law of large numbers. (Here, if you use
Chebechev’s inequality in your proof, then also include in your
answer a proof of Chebechev’s inequality.)
Use Hess’ Law and ΔH for the first two reactions: 1. NaOH (aq) +
HCl (aq) → H2O (l) + NaCl (aq) 2. NaOH (aq) + NH4Cl (aq) → NH3 +
NaCl + H2O (l) to determine ΔH for this reaction: NH3 + HCl →
NH4Cl
Here are four questions:
1. Prove a standard Brownian motion is Gaussian process .
2. Prove a Brownian bridge is Gaussian process.
3. Prove Ornstein-Uhlenbeck process is Gaussian
4. Prove the position process is Gaussian.
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