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Lecture12-06.3-Ideal_Gas_processes-7.1-Bose_condensate

# Lecture12-06.3-Ideal_Gas_processes-7.1-Bose_condensate -...

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1 Last time Classical Limit: Ideal Gas Chemical Potential Free Energy Pressure Internal Energy Entropy LECTURE 12 Last time Heat Capacity Ideal Gas with Internal DOF Diatomic Ideal Gas Experimental Verification of the Sackur-Tetrode Equation for a monatomic ideal gas LECTURE 12

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2 Today Chapter 6 (part 3) Ideal Gas: Expansion LECTURE 12 Processes of an ideal gas: Reversible Isothermal Expansion Reversible Isentropic Expansion Sudden (irreversible!) Expansion into Vacuum Bose Einstein Condensation (Chapter 7) Ideal Gas Processes Reversible Isothermal Expansion Reversible Adiabatic, Isentropic Expansion Sudden (irreversible!) Expansion into Vacuum Iso = Constant Constant Temperature; Have to allow heat in/out Constant Entropy; No heat allowed in or out A = Not Dia = through No heat allowed in or out; No work allowed
3 Thermodynamic Identity Change in internal energy is heat in minus work out plus particles in. Today, dN = 0 , and this becomes: For reversible processes, integrals are defined throughout the process. For irreversible processes, we can’t use them, because the system is out of equilibrium during the process, and we can’t define the variables. in out U d pdV Q W τ σ = - = - Reversible Isothermal Expansion Gas Piston Heat In Work Out Given: 1x10 22 atoms, Initial temperature T=300K Volume doubles during expansion The final pressure is 1/2 the initial pressure. What is the pressure after expansion?

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4 Reversible Isothermal Expansion Gas Piston Heat In Work Out Given: 1x10 22 atoms, Initial temperature T=300K Volume doubles during expansion What are the units of entropy? What is the change in entropy? Reversible Isothermal Expansion Gas Piston Heat In Work Out Given: 1x10 22 atoms, Initial temperature T=300K Volume doubles during expansion How much work does the gas do as it expands? ( ) log 2 28.7 J B W N k T = = Work out
5 Reversible Isothermal Expansion Gas Piston Heat In Work Out Given: 1x10 22 atoms, Initial temperature T=300K Volume doubles during expansion What is the internal energy of an ideal gas? What is the change of internal energy? Reversible Isothermal Expansion Gas Piston Heat In Work Out Given: 1x10 22 atoms, Initial temperature T=300K Volume doubles during expansion What is the change of free energy?

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Lecture12-06.3-Ideal_Gas_processes-7.1-Bose_condensate -...

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