◈ Termodinamica

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

📋 Formulario

Complete Theory

Worked Examples

Example 1Carnot engine — Maximum efficiency calculation
Example 2Otto cycle r=10r=10 — Efficiency of a spark-ignition engine

Exercises with Solutions

Exercise 1Real engine vs Carnot — How far from the limit?Hard
📋 Problem to solve
A heat engine operates between TH=650T_H=650 K and TC=290T_C=290 K. It absorbs QH=8Q_H=8 kJ and produces W=2.8W=2.8 kJ. Compute: (a) real efficiency η\eta; (b) Carnot efficiency ηCarnot\eta_{Carnot}; (c) entropy change of the universe ΔSuniv\Delta S_{univ}.
📌 Given data
T_H=650 KT_C=290 KQ_H=8000 JW=2800 J
Exercise 2Refrigerator — How much energy is needed to cool?Hard
📋 Problem to solve
A refrigerator maintains its interior at TC=3°CT_C=3°C in a room at TH=35°CT_H=35°C. It must remove QC=200Q_C=200 kJ/h from the interior. Compute: (a) maximum theoretical COP; (b) minimum required power; (c) heat QHQ_H rejected to the room.
📌 Given data
T_C=276 KT_H=308 KQ_C=200000 J/h
📚

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