◈ Termodinamica

Gas perfetti, trasformazioni termodinamiche, I e II principio, macchine termiche, cicli di Carnot e Otto, entropia.

📋 Formulario

Complete Theory

Worked Examples

Example 1Isobaric process — A gas expanding at constant pressure
Example 2RMS speed of nitrogen at 300 K — How fast are molecules?

Exercises with Solutions

Exercise 1Compound process (isobaric + isochoric)Hard
📋 Problem to solve
A monatomic gas (n=3n=3 mol, Cv=3R/2C_v=3R/2) undergoes: A(T=400T=400 K, P=2P=2 atm) →isobaric→ B(T=600T=600 K) →isochoric→ C(P=5P=5 atm). Find total work WtotW_{tot} and total internal energy change ΔUtot\Delta U_{tot}.
📌 Given data
n=3 molC_v=3R/2P_A = P_B = 2 atm (isobar)V_B = V_C (isochore)
Exercise 2Dalton's law — Gas mixturesHard
📋 Problem to solve
A container of volume V=10V=10 L at T=300T=300 K holds n1=0.5n_1=0.5 mol of O₂ and n2=1.2n_2=1.2 mol of N₂. Find total pressure, partial pressures, and mole fractions.
📌 Given data
V=0.010 m³T=300 Kn_O₂=0.5 moln_N₂=1.2 mol
📚

Recommended Books

Introductory
Heat and Thermodynamics
Zemansky & Dittman
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Integrative Problems

Problems combining all chapters — exam level
Problem 1The Thermoelectric Power Plant: from Gas to Molecules to EntropyEXTREME
A thermoelectric power plant uses n=5 moln = 5\,\mathrm{mol} of a diatomic gas (γ=7/5\gamma = 7/5, Cv=5R/2C_v = 5R/2) running through the following cycle on a PV diagram:

State A: PA=1 atmP_A = 1\,\mathrm{atm}, TA=300 KT_A = 300\,\mathrm{K}. A→B: adiabatic compression to VB=VA/8V_B = V_A/8 (compression ratio r=8r = 8). B→C: isochoric, heating to TC=2400 KT_C = 2400\,\mathrm{K} (combustion). C→D: adiabatic expansion to VD=VAV_D = V_A (return to original volume). D→A: isochoric, cooling (Otto cycle).
📌 Problem data
n = 5\,\mathrm{mol}\gamma = 7/5 = 1.4,\; C_v = 5R/2T_A = 300\,\mathrm{K},\; P_A = 1\,\mathrm{atm}r = V_A/V_B = 8T_C = 2400\,\mathrm{K}
(a)Ideal Gas — Thermodynamic States(b)First Law — Work and Heat for Each Process(c)Cycles — Otto vs Carnot Efficiency(d)Kinetic Theory — Molecules in Motion(e)Entropy — Second Law and Global Balance