57.2 Introduction to physical_constants

physical_constants is a collection of physical constants, copied from CODATA 2006 recommended values (https://physics.nist.gov/cuu/Constants/). load ("physical_constants") loads this package, and loads ezunits also, if it is not already loaded.

A physical constant is represented as a symbol which has a property which is the constant value. The constant value is a dimensional quantity, as represented by ezunits. The function constvalue fetches the constant value; the constant value is not the ordinary value of the symbol, so symbols of physical constants persist in evaluated expressions until their values are fetched by constvalue.

physical_constants includes some auxiliary information, namely, a description string for each constant, an estimate of the error of its numerical value, and a property for TeX display. To identify physical constants, each symbol has the physical_constant property; propvars(physical_constant) therefore shows the list of all such symbols.

physical_constants comprises the following constants.

%c

speed of light in vacuum

%mu_0

magnetic constant

%e_0

electric constant

%Z_0

characteristic impedance of vacuum

%G

Newtonian constant of gravitation

%h

Planck constant

%h_bar

Planck constant

%m_P

Planck mass

%T_P

Planck temperature

%l_P

Planck length

%t_P

Planck time

%%e

elementary charge

%Phi_0

magnetic flux quantum

%G_0

conductance quantum

%K_J

Josephson constant

%R_K

von Klitzing constant

%mu_B

Bohr magneton

%mu_N

nuclear magneton

%alpha

fine-structure constant

%R_inf

Rydberg constant

%a_0

Bohr radius

%E_h

Hartree energy

%ratio_h_me

quantum of circulation

%m_e

electron mass

%N_A

Avogadro constant

%m_u

atomic mass constant

%F

Faraday constant

%R

molar gas constant

%%k

Boltzmann constant

%V_m

molar volume of ideal gas

%n_0

Loschmidt constant

%ratio_S0_R

Sackur-Tetrode constant (absolute entropy constant)

%sigma

Stefan-Boltzmann constant

%c_1

first radiation constant

%c_1L

first radiation constant for spectral radiance

%c_2

second radiation constant

%b

Wien displacement law constant

%b_prime

Wien displacement law constant

Reference: https://physics.nist.gov/cuu/Constants/

Examples:

The list of all symbols which have the physical_constant property.

(%i1) load ("physical_constants")$
(%i2) propvars (physical_constant);
(%o2) [%c, %mu_0, %e_0, %Z_0, %G, %h, %h_bar, %m_P, %T_P, %l_P, 
%t_P, %%e, %Phi_0, %G_0, %K_J, %R_K, %mu_B, %mu_N, %alpha, 
%R_inf, %a_0, %E_h, %ratio_h_me, %m_e, %N_A, %m_u, %F, %R, %%k, 
%V_m, %n_0, %ratio_S0_R, %sigma, %c_1, %c_1L, %c_2, %b, %b_prime]

Properties of the physical constant %c.

(%i1) load ("physical_constants")$
(%i2) constantp (%c);
(%o2)                         true
(%i3) get (%c, description);
(%o3)               speed of light in vacuum
(%i4) constvalue (%c);
                                      m
(%o4)                     299792458 ` -
                                      s
(%i5) get (%c, RSU);
(%o5)                           0
(%i6) tex (%c);
$$c$$
(%o6)                         false

The energy equivalent of 1 pound-mass. The symbol %c persists until its value is fetched by constvalue.

(%i1) load ("physical_constants")$
(%i2) m * %c^2;
                                2
(%o2)                         %c  m
(%i3) %, m = 1 ` lbm;
                              2
(%o3)                       %c  ` lbm
(%i4) constvalue (%);
                                            2
                                       lbm m
(%o4)              89875517873681764 ` ------
                                          2
                                         s
(%i5) E : % `` J;
Computing conversions to base units; may take a moment. 
                     366838848464007200
(%o5)                ------------------ ` J
                             9
(%i6) E `` GJ;
                      458548560580009
(%o6)                 --------------- ` GJ
                         11250000
(%i7) float (%);
(%o7)              4.0759872051556356e+7 ` GJ