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- What is the temperature of a two-level system of energy separation equivalent to 400 cm−1 when the population of the upper state is one-third that of the lower state?What is the temperature of a two-level system of energy separation equivalent to 300 cm−1 when the population of the upper state is one-half that of the lower state?Identify the systems for which it is essential to include a factor of 1/N! on going from Q to q : (i) a sample of carbon dioxide gas, (ii) a sample of graphite, (iii) a sample of diamond, (iv) ice.
- Identify the systems for which it is essential to include a factor of 1/N! on going from Q to q : (i) a sample of helium gas, (ii) a sample of carbon monoxide gas, (iii) a solid sample of carbon monoxide, (iv) water vapour.2- There is a system consisting of N independent particles. Each particle can have only one of the two energy levels, -€g and +eo. Find the thermodynamic weight of a state with the total energy E = Meo (M = -N..+N), and discuss the statistical-thermodynamic properties of the system for the range E < 0, deriving specially the relation between temperature and the energy as well as the specific heat.EXERSICE 2 A system is characterized by two non-degenerate energy levels. At a temperature of 300 K, the probability of the first energy level is p₁ level p2 600 K. = 0.8 and of the second energy = 0.2. Calculate the probabilities of the two energy plants at a temperature of
- A nitrogen molecule, N2, is confined in a pool of potential energy. What is the lowest power state for this system?The fugacity of a monatomic gas is found to obey the relation ?(?, ?) = ????. Write expressions for the molar heat capacity at constant pressure.2. Consider a system with 1000 particles that can only have two energies, &, and ɛ, with E, > E,. The difference between these two values is Aɛ = ɛ, - & . Assume that gi = g2 = 1. Using the equation for the Boltzmann distribution graph the number of particles, ni and n2, in states &, and ɛ, as a function of temperature for a A6 = 1×10-21 J and for a temperature range from 2 to 300 K. (Note: kµ = 1.380×10 23 J K-!. " - & % n or = e n, 8,
- The internal energy of a system A None of these В is the sum of the rotational, vibrational, and translational energies of all of its components refers only to the energies of the nuclei of the atoms of the component molecules D is the sum of the kinetic energy of all of its components E) is the sum of the potential and kinetic energies of the components. The molar heat capacity of solids predicted by the Einstein model is given by hv e kBT hv Cy = 3R \kgT 2 hv 1-e kgT Determine the high-temperature limit of Cy, namely, lim Cy. T-00(1) The molecules in a thermally equilibrated isolated system are confined to just the two (non-degenerate) energy levels. lowest (a) Write down an expression for the partition function q of this system if the energy levels are separated by an amount ɛ. (b) If q = 1.142, determine the temperature of the system if the two energy levels are separated by 8 kJ/mol. (c) What is q in the limit of very high temperatures?