Base quantities for thermodynamic derivatives. More...
#include <part_deriv.h>
The quantities computed by heat_cap_ppart_const_press(),
computed by heat_cap_ppart_const_vol(),
computed by compress_const_tptr(),
computed by compress_adiabatic(), and
computed by coeff_thermal_exp are related by
and
For the derivatives below, the following Jacobian is useful
For convenience, we define the quantity
Another common combination of derivatives is
Definition at line 362 of file part_deriv.h.
Public Member Functions | |
template<class part_deriv_t > | |
double | heat_cap_ppart_const_vol (part_deriv_t &p, double temper) |
The heat capacity per particle at constant volume (unitless) More... | |
template<class part_deriv_t > | |
double | heat_cap_ppart_const_press (part_deriv_t &p, double temper) |
The heat capacity per particle at constant pressure (unitless) More... | |
template<class part_deriv_t > | |
double | compress_adiabatic (part_deriv_t &p, double temper) |
The adiabatic compressibility. More... | |
template<class part_deriv_t > | |
double | compress_const_tptr (part_deriv_t &p, double temper) |
The isothermal compressibility. More... | |
template<class part_deriv_t > | |
double | coeff_thermal_exp (part_deriv_t &p, double temper) |
The coefficient of thermal expansion. More... | |
template<class part_deriv_t > | |
double | squared_sound_speed (part_deriv_t &p, double temper) |
The squared sound speed (unitless) More... | |
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inline |
This function computes
in units of length.
To write this in terms of the three derivatives in o2scl::part_deriv_press,
Definition at line 571 of file part_deriv.h.
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inline |
This function computes
(sometimes referred to as or
)
To write this in terms of the three derivatives in o2scl::part_deriv_press,
The first Jacobian
and the second Jacobian was computed above. The result is
Definition at line 494 of file part_deriv.h.
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inline |
This function computes
(sometimes referred to as or
) in units of inverse length to the fourth power.
To write this in terms of the three derivatives in o2scl::part_deriv_press,
Definition at line 530 of file part_deriv.h.
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inline |
This function returns
To write this in terms of the three derivatives in o2scl::part_deriv_press,
The first Jacobian was computed above since
The second is
The final result is
This is for an ideal gas.
Definition at line 446 of file part_deriv.h.
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inline |
This function returns
To write this in terms of the three derivatives in o2scl::part_deriv_press,
This is for an ideal gas.
Definition at line 397 of file part_deriv.h.
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inline |
This function computes the squared sound speed (including relativistic effects)
The result is unitless. To get the units of a squared velocity, one must multiply by .
The nonrelativistic squared sound speed is
where is computed in compress_adiabatic() .
To write in terms of the three derivatives in o2scl::part_deriv_press,
The first Jacobian was computed above (up to a sign). The second is the determinant of
with
giving
The final result is
Definition at line 664 of file part_deriv.h.
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