◈ Termodinamica

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

📋 Formulario

Complete Theory

Worked Examples

Example 1Cycle A→B→C→A — Net work in a thermodynamic cycle
Example 2Ice → steam — The stages of heating

Exercises with Solutions

Exercise 1Adiabatic compression — The Diesel ignites by itselfHard
📋 Problem to solve
A diatomic gas (γ=1.4\gamma=1.4, n=2n=2 mol, Cv=5R/2C_v=5R/2) undergoes adiabatic compression from P1=1P_1=1 atm, T1=300T_1=300 K to P2=8P_2=8 atm. Find T2T_2, WW and ΔU\Delta U. Explain why the temperature rises so much.
📌 Given data
n=2 molγ=1.4C_v=5R/2P_1=1 atm, T_1=300 KP_2=8 atm
Exercise 2Entropy change in simple processesHard
📋 Problem to solve
Calculate ΔS\Delta S for: (a) isobaric heating of n=1n=1 mol diatomic gas (Cp=7R/2C_p=7R/2) from T1=300T_1=300 K to T2=600T_2=600 K; (b) isothermal expansion at T=300T=300 K with V2=2V1V_2=2V_1 for the same gas.
📌 Given data
n=1 molC_p=7R/2T_1=300 K, T_2=600 KV_2/V_1=2
📚

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