Concentratia moleculara — formulă fizică BAC (Termodinamica) — PBFizica

Notiuni de baza

Unitatea de masa atomica

1 \; u = 1{,}66 \times 10^{-27} \; \text{kg}

Masa molara, nr. de moli, nr. Avogadro

\upsilon = \frac{m}{\mu} = \frac{N}{N_A} = \frac{V}{V_\mu}

$N_A = 6{,}023 \times 10^{23} \; \text{mol}^{-1}$ , $V_{\mu_0} = 22{,}42 \times 10^{-3} \; \text{m}^3/\text{mol}$

Parametri de stare

Volumul

V = S \cdot l \qquad [V]_{SI} = \text{m}^3

Presiunea

p = \frac{F}{S} \qquad [p]_{SI} = \text{Pa} = \text{N/m}^2

$1 \; \text{atm} = 101\,325 \; \text{Pa}$ , $1 \; \text{bar} = 10^5 \; \text{Pa}$

Presiunea hidrostatica

p = \rho \cdot g \cdot h

Temperatura

T \; [K] = t \; [°C] + 273

Densitatea

\rho = \frac{m}{V} \qquad [\rho]_{SI} = \text{kg/m}^3

Concentratia moleculara

n = \frac{N}{V} \qquad [n]_{SI} = \text{m}^{-3}

Transformarile gazului ideal

Ecuatia termica de stare

p \cdot V = \upsilon \cdot R \cdot T \qquad R = 8{,}31 \; \text{J} / (\text{mol} \cdot \text{K})

Transformarea izoterma (T = ct.) — Boyle-Mariotte

p \cdot V = \text{const.} \qquad p_i V_i = p_f V_f

Transformarea izobara (p = ct.) — Gay-Lussac

\frac{V}{T} = \text{const.} \qquad \frac{V_i}{T_i} = \frac{V_f}{T_f}

Transformarea izocora (V = ct.) — Charles

\frac{p}{T} = \text{const.} \qquad \frac{p_i}{T_i} = \frac{p_f}{T_f}

Transformarea generala

\frac{p \cdot V}{T} = \text{const.} \qquad \frac{p_i V_i}{T_i} = \frac{p_f V_f}{T_f}

Energia interna

Energia termica a unei molecule

\varepsilon_T = \frac{i}{2} \, k T \qquad k = 1{,}38 \times 10^{-23} \; \text{J/K}

Grade de libertate

Tip gaz	Grade de libertate $i$
Monoatomic	3
Biatomic	5
Poliatomic	6

Ecuatia calorica de stare

U = \frac{i}{2} \, \upsilon R T

Viteza termica a moleculelor

v_T = \sqrt{\frac{3kT}{m_0}} = \sqrt{\frac{3RT}{\mu}}

Formula fundamentala a teoriei cinetico-moleculare

p = \frac{2}{3} \, n \, \varepsilon_T

Forma primara a ecuatiei termice

p = n \cdot k \cdot T \qquad k \cdot N_A = R

Lucrul mecanic in termodinamica

Lucrul mecanic

L = \int_{V_i}^{V_f} p \, dV

Lucrul mecanic pe transformari

Transformare	Lucrul mecanic $L$
Izocora	$L = 0$
Izobara	$L = p \cdot \Delta V = \upsilon R \Delta T$
Izoterma	$L = \upsilon R T \ln \dfrac{V_f}{V_i}$
Adiabatica	$L = -\Delta U = -\upsilon C_V \Delta T$

Principiul I al Termodinamicii

Principiul I

Q = \Delta U + L

Caz	Consecinta
Adiabatic ( $Q = 0$ )	$L = -\Delta U$
Ciclic ( $\Delta U = 0$ )	$Q = L$

Coeficienti calorici

Capacitatea calorica

C = \frac{Q}{\Delta T} \qquad [C]_{SI} = \text{J/K}

Caldura specifica

c = \frac{Q}{m \cdot \Delta T} \qquad [c]_{SI} = \text{J} / (\text{kg} \cdot \text{K})

$c_{\text{apa}} = 4180 \; \text{J} / (\text{kg} \cdot \text{K})$ , $1 \; \text{cal} = 4{,}18 \; \text{J}$

Caldura molara

C_\mu = \frac{Q}{\upsilon \cdot \Delta T} \qquad [C_\mu]_{SI} = \text{J} / (\text{mol} \cdot \text{K})

Caldurile molare Cv si Cp

C_V = \frac{i}{2} \, R \qquad C_P = \frac{i+2}{2} \, R

	Monoatomic	Biatomic	Poliatomic
$C_V$	$\dfrac{3}{2}R$	$\dfrac{5}{2}R$	$3R$
$C_P$	$\dfrac{5}{2}R$	$\dfrac{7}{2}R$	$4R$
$\gamma = C_P / C_V$	$5/3$	$7/5$	$4/3$

Relatia Robert–Mayer

C_P - C_V = R

Exponentul adiabatic

\gamma = \frac{C_P}{C_V} \qquad p \cdot V^\gamma = \text{const.}

Q, ΔU, L — Tabel sinteza

Transformare	$Q$	$\Delta U$	$L$
Izocora	$\upsilon C_V \Delta T$	$\upsilon C_V \Delta T$	$0$
Izobara	$\upsilon C_P \Delta T$	$\upsilon C_V \Delta T$	$p \Delta V = \upsilon R \Delta T$
Izoterma	$\upsilon R T \ln(V_f/V_i)$	$0$	$\upsilon R T \ln(V_f/V_i)$
Adiabatica	$0$	$\upsilon C_V \Delta T$	$-\upsilon C_V \Delta T$

Principiul II — Masini termice

Lucrul masinii termice

L = Q_p - |Q_c|

Randamentul masinii termice

\eta = \frac{L}{Q_p} = 1 - \frac{|Q_c|}{Q_p} < 1

Ciclul Carnot

\eta_C = 1 - \frac{T_r}{T_c}

$T_c$ = temperatura sursei calde, $T_r$ = temperatura sursei reci

Motorul Otto

\eta_{\text{Otto}} = 1 - \frac{1}{\varepsilon^{\gamma - 1}} \qquad \varepsilon = \frac{V_1}{V_2}

Ciclu: 2 adiabatice + 2 izocore. $\varepsilon$ = raport de compresie.

Motorul Diesel

\eta_{\text{Diesel}} = 1 - \frac{1}{\varepsilon^{\gamma-1}} \cdot \frac{\sigma^\gamma - 1}{\gamma(\sigma - 1)}

$\varepsilon = V_1/V_2$ , $\sigma = V_3/V_2$ . Ciclu: 2 adiabatice + 1 izobara + 1 izocora.