(a) Obtain total partition function for an Ideal di-atomic gas and use it to drive the expression of specific heat
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- This is the expression valid for van der Waals gases. Calculate the final temperature if the Joule’s free expansion experiment was carried out to double the volume of 1 L gas at 25 °C with a) He b) CO2 molecules. The van der Waals coefficients, a, for He and CO2 are 0.0346 and 3.658, respectively. (Hint: Use equipartition to calculate Cv values and assume three of the vibrations not populated in carbon dioxide)According to the energy according to the equipartition theorem of degrees of freedom, what is the internal energy of 5 moles of rigid diatomic ideal gas molecules at equilibrium at temperature T?A 0.825 mol sample of NO, (g) initially at 298 K and Molar heat capacity at constant volume (Cy,m) R Туре of gas 1.00 atm is held at constant volume while enough heat is applied to raise the temperature of the gas by 10.3 K. atoms Assuming ideal gas behavior, calculate the amount of heat linear molecules (q) in joules required to affect this temperature change and nonlinear molecules 3R the total change in internal energy, AU. Note that some where R is the ideal gas constant books use AE as the symbol for internal energy instead of AU. q = J AU = J
- Problem 3: Starting with the expression derived in the lecture notes for the multiplicity of an ideal 1 n3N/2 (2m)³N/2 N! (3N/2)! h3N gas VNU3N/2 derive the Sackur-Tetrode expression for the entropy.By considering the number of accessible states for an ideal two-dimensional gas made up of N adsorbed molecules on a surface of area A, obtain an expression for the entropy of a system of this kind. Use the entropy expression to obtain the equation of state in terms of N, A, and the force per unit length F. What is the specific heat of the two-dimensional gas at constant area?The natural variables for the internal energy U are the entropy S and the volume V. This means that, if you know S and V, you can find U(S, V) and simple expressions for T and P. Supposed instead that you know U(T, V). Show that this leads to the following expression for P: -/), dT + f(V) T aV T2 where f(V) is an arbitrary function of V.
- Please solve and explian the solution: Let M represent a certain mass of coal which we assume will deliver 100 joules of heat when burned – whether in a house, delivered to the radiators or in a power plant, delivered at 1000°C. Assume the plant is ideal (no waste in turbines or generators) discharging its heat at 30°C to a river. How much heat will M, burned at the plant to generate electricity, provide for the house when the electricity is:(a) delivered to residential resistance-heating radiators?(b) delivered to a residential heat pump (again assumed ideal) boosting heat from a reservoir at 0°C into a hot-air system at 30°C?For a dilute gas of N monatomic particles with mass m and total energy E, use the Sackur- Tetrode equation for the entropy S V = log + NkB to derive expressions for the pressure and internal energy in terms of the temperature T and volume V. [You may use that X₁ = 3πh² N/(mE).] th