MSE 3050, Phase Diagrams and Kinetics, Leonid Zhigilei0°C 200°CABadiabatic enclosureP = 1 atm1.One mole of aluminum at a uniform temperature of 0ºC is placed in thermal contact with a second mole of aluminum which, initially, is at a uniform temperature of 200ºC. The pressure in the system is maintained at 1 atm. The two moles of aluminum are thermally insulated from the surroundings. Temperature dependence of the constant pressure heat capacity of solid aluminum can be described by the following expression:cp= 20.67 + 12.38×10-3T J/mole K. (a) Calculate the common temperature of the 2 mole system, which is contained in an adiabatic enclosure, when the thermal equilibrium is attained. (b) How much heat is transferred between the two parts of the system?(c) How much entropy is produced by the transfer? Homework #2 (page 1 of 2)2. Calculate the difference in the molar enthalpies of δ-Fe and γ-Fe (ΔHγ→δ= Hδ-Hγ) at 1600 K. The equilibrium transition temperature between γ-Fe & δ-Fe is Tγ→δ= 1664 KThe molar heat of γ-Fe to δ-Fe phase transformation at 1664 K is ΔHγ→δ= 840 J/molYou can assume temperature independent values of heat capacities of the γ-Fe and δ-Fe: cPγ= 35.5 J/mol KcPδ= 43.9 J/mol KYou can also assume that the constant values of the heat capacity are also applicable at temperatures where the phases are metastable.MSE 3050, Phase Diagrams and Kinetics, Leonid ZhigileiHomework #2 (page 2 of 2)3. Consider a small cube of silver enclosed in a heat reservoir so large that small transfer of heat from/to silver does not change its temperature, 1400 K. Calculate the total entropyproduced in the silver-reservoir adiabatic system when 1 mole of crystalline silver melts at 1400 K and 1 atm pressure. Assume temperature independent heat capacities cp= 32.6 J/K/mol for solid silver and cp= 30.5 J/K/mol for liquid silver. The equilibrium melting temperature of silver is Tm= 1234 K.Molar heat of melting is ∆Hm= 11090 J/mol.Based on the result of your calculation and the 2ndlaw of thermodynamics conclude whether silver will melt spontaneously at 1400 K.4.A A gas at room temperature and constant pressure of 1 atm is going to be used to heat a material that is colder than the gas. There are two options - to use 1 mol of Ar gas or 1 mol of N2gas for this purpose. Which gas will ensure higher temperature of the material after thermal equilibration with the gas? Briefly explain your answer.4.B A new gaseous species has been made in the laboratory. The number of atoms in each molecule is unknown. Measurements of the heat capacity at constant pressure yield a value of ~4.5R at high temperatures (when quantum corrections to the molecular dynamics can be neglected) and low values of pressure (when the contribution of intermolecular interactions to the heat capacity can be neglected). What is the number of atoms in each molecule? Briefly explain your answer.4.C The strength of interatomic bonding in two elemental crystalline materials is approximately the same, but Material #1 is composed of atoms that are approximately 4 times heavier compared to Material #2. Sketch schematically the temperature dependences of the heat capacities of the two materials on the same plot for a range of temperatures from 0K to a temperature that is substantially above the Debye temperatures of both