The Hamiltonian for classical ideal gas for N atoms is H = (i) Calculate E(E) and obtain the following entropy relation 3/21 (4rm E 3h2 N. S(E,V) = Nklog +-Nk (ii) Calculate internal energy U(S,V). (iii) Calculate specific heat capacity.

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: a T³V 23=

A: Partition Function is,   Then pressure can be calculated as,

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: 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: Consider a van der haal's that undergoes gas an 18othermal expansion focm Volume V, to Volume Vz 9…

A:

Q: (1) When the energy of a system (simple harmonic oscillator) is given by E = heat bath of (constant)…

A:

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

A: I have written formula

Q: Consider a system of two Einstein solids with 10 ocillators in A and B each, and a total of 40 units…

A: Consider the given data as below. Number of oscillators in solid A, NA=10 Number of oscillators in…

Q: Does the internal energy (U) of a perfect gas go up or down with increasing pressure under…

A:

Q: For an isothermal reversible expansion of two moles of an ideal gas, what is the entropy change of…

A: Number of moles: To calculate the entropy change of the gas and the surroundings during an…

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

A:

Q: By considering how the total entropy changes at fixed temperature, show that particles will flowfrom…

A:

Q: Polymers, like rubber, are made of very long molecules, usually tangled up in a configuration that…

A: (a) Each link has only two possible states, and they point either left or right. Let  be the number…

Q: vii) Consider a case of a particles and two compartments, if m is the oumber of partacles in one…

A: Given, Total number of particles=n In one compartment, no of particle s is n1. In the other…

Q: -Consider a lassi cal ideal gas Comsisting of N atoms of mass M in thermal equui'li bniem at Canprte…

A:

Q: Starting with the Clausius Inequality, ∂S ≥ ∂q/T, can you prove that, under conditions of constant…

A:

Q: a Inz' Show that PK, = 1- P() for a real gas where Kr is the isothermal compressibility.

A: Given, kT is isothermal compressibilitykT= -1v∂v∂PT  ....(1)

Q: Consider an ideal monatomic gas. Here, take N as constant. We can take any two arguments like (p, V)…

A: A) Given that  internal energy is: E or U = 32NkT and dU =32NkdT Using (1) , dU =dQ -dW…

Q: J WAB W AB J W BC J WAD W DC

A: Given figure as, Here, 1 atm= 101325 Pa 1l= 10-3m3

Q: Determine the amount by which the star's thermal radiation increases the entropy of the entire…

A: Entropy The entropy change of a system if ∆Q amount of heat is absorbed by the system at temperature…

Q: Consider a star that is a sphere with a radius of 6.38  108 m and an average surface temperature of…

A: Given data: Radius R =6.38×108 m Star's temperature T= 5200 K Universe's temperature T'= 2.73 K

Q: Consider the high temperature rotational partition function. 1 BA where A is a constant related to…

A: We are given partition function for some molecule. Here β=1kT Where T is temperature. The average…

Q: (1) When the energy of the system (simple harmonic oscillator) is given by E = (n +;) hw in a heat…

A: The partition function is given as, Z=∑n=0∞e-EnkT Thus,…

Q: Answer in 90 minutes please.

A:

Q: lculate the work for an ideal gas that expands isothermally at T0 from V1 to V2.

A:

Q: Each particle has 2 energy levels that are 0 and α. Using ni=Ae^−εi/kT What is the entropy S of…

A:

Q: Which type or types of energy will have the greatest contribution to the molar entropy of N2 at 298…

A: The molar entropy of any substance is defined as the entropy of the pure substance at standard…

Q: By considering how the total entropy changes at fixed temperature, show that particles will flow…

A: To show that particles will flow from system  A  to system  B  if the chemical potentials…

Q: |Calculate the change in entropy in cal/K for a sample of water with mass m= 1.6 kg and changing…

A: mass of water m = 1.6 kg initial temperature is T1 = 24.2 oC = 24.2 + 273.15 =  297.35 K final…

Q: Answer in 90 minutes please.

A: Step 1: Step 2: Step 3: Step 4:

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: Consider a system of two levels E1= 0, g1= 1 and E2= 1.6 X102ºJ, g2 = 2 is populated by %3D N atoms…

A: Two energy levels E1 = 0, g1 = 1  E2 = 1.6 × 10- 20 J, g2 = 2   Total number of atoms = N

Q: Consider two distinguishable particles, each of which can have energy nε with n = 0, 1, 2, .... By…

A: Step 1: Step 2: Step 3: Step 4:

Q: system of three particles can possess four energies 0, E, 2E, and 4E with degeneracy 1,3,5,6…

A: The partition of the system is given by Where gi = Degeneracy of the state, Ei = Energy of the…

Q: A highly non-ideal gas has an entropy given by S=aNU/V, where the internal  energy, U is a function…

A: A highly non-ideal gas has an entropy given by S=aNUV, Where the internal energy, U, is a function…

Q: In Debye Approximation the entropy at some temperature T (less than 10 K) is aT(Blank 1 ) /3 If the…

A: The entropy at some temperature is given by E=aTn3…

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

A:

Q: Learning Goal: To derive the expression for the work done by an expanding gas, W-PAV, and to…

A:

Q: Maxwell BoHZmonn distriburion for an ideal gas is given bys P2 f(p) = ce %3D a) >Entropy for an can…

A: Given, Maxwell's distribution function for ideal gas is, Now solving for c, Then,