OII 2011 Nazionale Teorica

Alcune Costanti Fisiche ($\star$)

COSTANTE	SIMBOLO	VALORE	UNITÀ
Velocità della luce nel vuoto	$c$	$3.00\times 10^8$	${\text{m s}}^{-1}$
Carica elementare	$e$	$1.602\times 10^{-19}$	C
Massa dell’elettrone	$m_e$	$9.11\times 10^{-31}$	kg
		$=5.11\times 10^2$	$\text{keV }{c}^{-2}$
Costante dielettrica del vuoto	${ϵ}_0$	$8.85\times 10^{-12}$	${\text{F m}}^{-1}$
Permeabilità magnetica del vuoto	${\mu }_0$	$1.257\times 10^{-6}$	${\text{H m}}^{-1}$
Massa del protone	$m_p$	$1.673\times 10^{-27}$	kg
		$=9.38\times 10^2$	$\text{MeV }{c}^{-2}$
Costante di Planck	$h$	$6.63\times 10^{-34}$	J s
Costante universale dei gas	$R$	$8.31$	${\text{J mol}}^{-1}{\text{K}}^{-1}$
Numero di Avogadro	$N$	$6.02\times 10^{23}$	${\text{mol}}^{-1}$
Costante di Boltzmann	$k$	$1.381\times 10^{-23}$	${\text{J K}}^{-1}$
Costante di Faraday	$F$	$9.65\times 10^4$	${\text{C mol}}^{-1}$
Costante di Stefan–Boltzmann	$\sigma$	$5.67\times 10^{-8}$	${\text{W m}}^{-2}{\text{K}}^{-4}$
Costante gravitazionale	$G$	$6.67\times 10^{-11}$	${\text{m}}^3{\text{kg}}^{-1}{\text{s}}^{-2}$
Accelerazione di gravità standard	$g_0$	$9.81$	${\text{m s}}^{-2}$
Pressione atmosferica standard	$p_0$	$1.013\times 10^5$	Pa
Temperatura standard ($0{}^{\circ }\text{C}$)	$T_0$	$273$	K
Volume molare di un gas perfetto in condizioni standard ($p_0$, $T_0$)	$V_m$	$2.24\times 10^{-2}$	${\text{m}}^3{\text{mol}}^{-1}$
Unità di massa atomica	$u$	$1.661\times 10^{-27}$	kg

Altri dati che possono essere necessari ($\star$)

	SIMBOLO	VALORE	UNITÀ
Raggio terrestre	$R_T$	$6.38\times 10^3$	km
Densità dell’acqua	$d_a$	$1.00\times 10^3$	${\text{kg m}}^{-3}$
Calore specifico dell’acqua	$c_a$	$4.19\times 10^3$	${\text{J kg}}^{-1}{\text{K}}^{-1}$
Calore di fusione dell’acqua	${\lambda }_f$	$3.34\times 10^5$	${\text{J kg}}^{-1}$
Calore di vaporizzazione dell’acqua (a $100{}^{\circ }\text{C}$)	${\lambda }_v$	$2.26\times 10^6$	${\text{J kg}}^{-1}$
Calore specifico del ghiaccio (a $0{}^{\circ }\text{C}$)	$c_g$	$2.11\times 10^3$	${\text{J kg}}^{-1}{\text{K}}^{-1}$

($\star$) Valori arrotondati, con errore relativo minore di $10^{-3}$

Topic: Newtonian Mechanics, Oscillations & Waves, Thermodynamics Metodi: Free-Body Diagram, Kinematic Equations, Vector Decomposition, Simple Harmonic Motion Analysis Competenze: Diagrammatic Reasoning, Mathematical Modeling Objects: — Fonte: Testo (PDF) — p.1 Soluzione: Soluzioni (PDF)

Some Physical Constants ($\star$)

CONSTANT	SYMBOL	VALUE	UNIT
Speed of light in vacuum	$c$	$3.00\times 10^8$	${\text{m s}}^{-1}$
Elementary charge	$e$	$1.602\times 10^{-19}$	C
Electron mass	$m_e$	$9.11\times 10^{-31}$	kg
		$=5.11\times 10^2$	$\text{keV }{c}^{-2}$
Vacuum permittivity	${ϵ}_0$	$8.85\times 10^{-12}$	${\text{F m}}^{-1}$
Vacuum permeability	${\mu }_0$	$1.257\times 10^{-6}$	${\text{H m}}^{-1}$
Proton mass	$m_p$	$1.673\times 10^{-27}$	kg
		$=9.38\times 10^2$	$\text{MeV }{c}^{-2}$
Planck constant	$h$	$6.63\times 10^{-34}$	J s
Universal gas constant	$R$	$8.31$	${\text{J mol}}^{-1}{\text{K}}^{-1}$
Avogadro number	$N$	$6.02\times 10^{23}$	${\text{mol}}^{-1}$
Boltzmann constant	$k$	$1.381\times 10^{-23}$	${\text{J K}}^{-1}$
Faraday constant	$F$	$9.65\times 10^4$	${\text{C mol}}^{-1}$
Stefan–Boltzmann constant	$\sigma$	$5.67\times 10^{-8}$	${\text{W m}}^{-2}{\text{K}}^{-4}$
Gravitational constant	$G$	$6.67\times 10^{-11}$	${\text{m}}^3{\text{kg}}^{-1}{\text{s}}^{-2}$
Standard acceleration of gravity	$g_0$	$9.81$	${\text{m s}}^{-2}$
Standard atmospheric pressure	$p_0$	$1.013\times 10^5$	Pa
Standard temperature ($0{}^{\circ }\text{C}$)	$T_0$	$273$	K
Molar volume of an ideal gas at standard conditions ($p_0$, $T_0$)	$V_m$	$2.24\times 10^{-2}$	${\text{m}}^3{\text{mol}}^{-1}$
Atomic mass unit	$u$	$1.661\times 10^{-27}$	kg

Other data that may be needed ($\star$)

	SYMBOL	VALUE	UNIT
Earth radius	$R_T$	$6.38\times 10^3$	km
Density of water	$d_a$	$1.00\times 10^3$	${\text{kg m}}^{-3}$
Specific heat of water	$c_a$	$4.19\times 10^3$	${\text{J kg}}^{-1}{\text{K}}^{-1}$
Latent heat of fusion of water	${\lambda }_f$	$3.34\times 10^5$	${\text{J kg}}^{-1}$
Latent heat of vaporization of water (at $100{}^{\circ }\text{C}$)	${\lambda }_v$	$2.26\times 10^6$	${\text{J kg}}^{-1}$
Specific heat of ice (at $0{}^{\circ }\text{C}$)	$c_g$	$2.11\times 10^3$	${\text{J kg}}^{-1}{\text{K}}^{-1}$

($\star$) Rounded values, with relative error less than $10^{-3}$

Solution: Soluzioni (PDF)