Derive the heat capacity Cv of a system whose canonical partition function is Z = AVNT³N where A is a temperature-independent constant.

You are studying a gas known as "gopherine" and looking in the literature you find that someone has reported the partition function for one molecule of this gas, 5/2 AzT q(V, T) = ) %3D h?m Assume that the molecules are independent and indistinguishable. Derive the expressions for the energy, (E), for this gas. Give your answers in terms of N, kg, T. V and the constants A and B. O (E) = NkaT ㅇ (E) =D NkaT ㅇ (E) %3D NkaT- O (E) = ANKET - O (E) = - T ㅇ (E)=D 쑤-

Using the method of the preceding problem, estimate the fraction of nitric oxide (NO) molecules at a temperature of 250 K that have energies between 3.451021 J and 3.501021 J. `

An approximate partition function for a gas of hard spheres can be obtained from the partition function of a monatomic gas by by V-b, where b is related to the volume of the W hard spheres. Derive expressions for the energy and the pressure of this system. (Use the following as necessary: b, kg, N, T, and V.) replacing V in Q(N, V, B) = [9(V, P)] (where q(V, B) = (22m) 3/2v) by V N! h²ß (E) (P) =

Write the mathematical relationships for each of the following Conclude the thermodynamic properties (parameters) of ideal gas same as ( energy , prussure, entropy , specific heat at fixed prussure , specific heat at fixed volume ) e 12:31 V

a) Find the difference of molar-specific heats Cp - C, for the gas covered by the equation of state: (P+) (V - b) = RT b) Determine the volume of the hypersphere in N-dimensional space. c) An ideal gas consists of N monatomic molecules. Using the grand canonical ensemble, (T-μ) distribution, calculate the chemical potential, pressure, and entropy.

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?

Could you sketch a distribution function of gaseous with respect to liquid water as a function of temperature (no formula, just a sketch)

Give the temperature T of 1 mole of ideal gas as a function of the pressure P, volume V,  and the gas constant R and give the internal energy U of a rigid diatomic ideal gas as a function of its temperature T and the gas constant R.

Using MATLAB editor, make a script m-file which includes a header block and comments: Utilizing the ideal gas law: Vmol= RT/P Calculate the molecular volume where: R = 0.08206 L-atm/(mol-K) P = 1.015 atm. and T = 270 - 315 K in 5 degree increments Make a display matrix which has the values of T in the first column and Vmol in the second column Save the script and publish function to create a pdf file from the script in a file named "ECE105_Wk2_L1_Prep_1"