To perform sensitivity analysis involving an integer linear program, it is best to use the same approach as you would for a linear program. use LP Relaxation. make multiple computer runs. use the dual prices very cautiously.

Q: Why is the entropy higher for a system with 5 particles with energy states >1 than for a system with…

A: Entropy increases precisely for energy states>1 because energy is conserved.     To hold a…

Q: . In class on Wednesday, we defined the availability as A = U + POV - ToS, where Po is the pressure…

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Q: (a) Answer the following questions about entropy-volume relationships: (i) For a general system, use…

A: (a) Helmholtz free energy is  A=U-TS Derivative is  dA=dU-TdS-SdT…

Q: (a) Show that the entropy o of a system in cannonical ensemble can be represented by- o = Σ P₁ log…

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Q: The probability p; of occupying an available state j is: Pj 9je-BEj Z where g; is the degeneracy of…

A: Step 1:The probability of occupying states i and k, respectively…

Q: The partition function of a hypothetical system is given by In Z = «TªV where a is a constant.…

A: A partition function measures the proportion of phase space occupied by the system. Basically, it…

Q: Calculate the change in Gibbs and Helmholtz free energies for one mole of an ideal gas that…

A: As, the temperature is constant, change in P will eventually results in change in V. Now, we know…

Q: A system consisting of six indistinguishable particles obeys the Fermi-Dirac statistics. This system…

A: Given that there are 6 particles which follows Fermi-dirac statistics. Degeneracy of each level is…

Q: Estimate the relative probabilities of various velocities. Pick a small interval ∆vx = 0.002vx rms.…

A: Given: Small interval dvx=0.002vxrms . It is known that the probability g(vx )dvx that the…

Q: 1-49. Maximize N! W(N1, N2,..., NM) = IN,! with respect to each N, under the constraints that EN,=N…

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Q: Consider system with just two states. Take the two states to have energies 0 and ε. Partition…

A: I have written formula

Q: A particle of mass m is bound in a one-dimensional well with one impenetrable wall. The potential…

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Q: From the two-level partition function: q = 1+ ekr obtain the total energy of N two-level systems.…

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Q: A system with charge (number of electrons) is placed in an electric field with potential E (volts).…

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Q: E △E=2×10-21 J DE=10-21 J E2 E1 Eo

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Q: 3. Use the Taylor series to estimate f (x) = e¬* at xi+1 1 for xi = 0.25. Employ the zero-, ||

A: Given: The function is e-x, The value of xi+1 is 1. The value of xi is 0.25. Introduction: The…

Q: Show that the coefficients of performance of refrigerators and heat pumps are related by COPref =…

A: Given : To prove  COPref = COPhp - 1

Q: 1. Consider a system of N localized non-interacting 1 – d quantum harmonic oscillators with…

A: We have to write the partition function is simple harmonic oscillator and also find its specific…

Q: For this modified van der Waals equation (with n and b as constants), find the following two partial…

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Q: In a canonical ensemble, how does the entropy relate to the thermodynamic probabilities of various…

A: Canonical ensemble :-                                       If all microstates corresponding to a…

Q: sion of 73 mJ/m² . A stable f vith 0.2 mm radii and film thi ow much was the liquid surfa

A: Gibbbs-Marangoni effect is the mass transfer along an interface between two fluids due to a…

Q: Obtain a power series expansion for f(z) = 1+ z 1– z in a disc D(0, r1) and stating what the maximum…

A: We have been provided with function f(z)=1+z1-z We have to obtain the power series expansion of…

Q: Imagine that your dog has eaten the portion that gives entropy data; only the enthalpy data remains.…

A: Entropy of the steam can be calculated by using the following formula. Here, is the latent heat of…

Q: To a good approximation, the vibrational states of a diatomic molecule can be approximated by that…

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Q: Four bones of eqyual 3) sizes are to distinquishable particles Find the probability of macyostate…

A: i) The most probable state is (3, 4, 1) when one particle moves from left to right, and probability…

Q: How will you express some state variables as partial derivatives of the Gibbs free energy G = U – TS…

A: The Gibbs free energy is given by, G=U-TS-YX State variables are the set of variables that describes…

Q: A mono-energetic, linear source emits S n/cm • s in an infinitely long cylindrical medium of radius…

A: Given that A mono energetic , linear source emits S neutron per centimeter sec in a long cylindrical…

Q: Gibbs definition of entropy is S=-k Law of Thermodynamics? B P,In(P)- what is the distribution at 0…

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Q: Consider N identical harmonic oscillators (as in the Einstein floor). Let the allowed energies of…

A: The energy of the system is given as  E=nhfZ=partition function of a single oscillatorZ=∑n=0∞  e-βEn…

Q: Q-Obtain expression of transition coefficient for a two level system up to first order, in the…

A: Consider a state Ψ of a two-level system with energies Ea and Eb. When there comes transition…

Q: 9x = exp(-/Bhv) 1- exp(-ßhv) Derive the partition function for a single harmonic oscillator in three…

A: Required  derivation of partition function for simple harmonic oscillator.

Q: If the adiabatic constant is 1.7 and the efficiency of Otto cycle is 73% then .the compression ratio…

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Q: Derive the heat capacity Cv of a system whose canonical partition function is Z = AVNT³N where A is…

A: To derive the heat capacity ( Cv) from the canonical partition function,Z=AVNT3NWe first determine…

Q: There are three fair coins in a bag. Two of them are normal (with a coin flip) and the third has a…

A: Total number of coins= 3 Number of biased coins=1  Number of normal coins= 2

Q: Consider a discrete random variable X with 2n+1 symbols xi, i = 1, 2, …, 2n+1. Determine the upper…

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Q: 5....Only the partition function as a function of temperature is required in order to determine the…

A: To find the energy of N particle system in a volume is it enough to find partition function as a…

Q: Describe the equipartition theorem, which holds in classical (non-quantum) thermodynamics for…

A: Equipartition theorem for classical thermodynamic system states that each degree of freedom that…

Q: In the canonical ensemble, we control the variables T, p, and N, and the fundamental function is the…

A: Solution: In the canonical ensemble, we control the variables T, p, and N, and the fundamental…

Q: tropy H(X | Y ) in terms of the joint distribution and associated conditional probabilit

A: Let us consider p(x, y) to be the joint probability distribution of the two random variables X and Y…