Q2/ For the harmonic oscillator in classical limit, if the partition function is given by Z(B) = 1/(ßħw)", find the entropy and internal energy. Q3/ Prove that F = -KTlnz .
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- (c) Determine the average (internal) energy of the system, ⟨?⟩.Consider two blocks of copper. Block A contains 800 atoms and initially has a total of 20 quanta of energy. Block B contains 200 atoms and initially has 80 quanta of energy. The two blocks are placed in contact with each other, inside an insulated container (so no thermal energy can be exchanged with the surroundings).After waiting for a long time (for example, an hour), which of the following would you expect to be true? A. The entropy of block A is equal to the entropy of block B. B. Approximately 50 quanta of energy are in block A, and approximately 50 quanta of energy are in block B. C. Approximately 80 quanta of energy are in block A, and approximately 20 quanta of energy are in block B. D. The temperature of block A and the temperature of block B are equal.Rather than insisting that all the molecules be in the left half of a container, suppose we only require that they be in the leftmost 99% (leaving the remaining 1% completely empty). What is the probability of finding such an arrangement if there are 100 molecules in the container? What if there are 10,000 molecules? What if there are 1023 ?
- •2.6 (c)-(f) • (c) Show that the grand canonical partition function of an ideal gas can be written as Zg = exp expleßu 23 (d) Use the expression for Zg to calculate the mean value for N, P, S, and show that PV = NkgT and that the Gibbs-Duhem equation gives E = ?NkgT.V₁₂: V₁ = 4:1 V₁ V₂ There are 6 molecules of a gas in V₂ and none in V₁. Now a hole i made in partition. Find the probability of finding 3 molecules on each side of the partition.8
- The variation of the molar Gibbs free pn- ergy of a substance with temperature and pressure is given by () T5/2 G = -T In Determine S, H, V, U and F.Imagine a photon gas at an initial temperature of T = 1.4 K. What is the temperature of the photon gas (in K) after it has undergone a reversible adiabatic expansion to 2 times its original volume?V7
- The exact differential for the Gibbs energy is given by dG = -SdT + VdP. The form of this differential implies which of the following relationships? O (7),- (), ƏG Әт ƏG др P T (37), - - (-), P T as ( x) - (*), = др T (327), = -(0)₁ == P TThe probability of finding an N2 molecule at ambient temperature at 515 m/s is zero. True or False?