### 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

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