Calculations

Calculations

GNU units conversion program
These calculations were made using the GNU units conversion program (manual) for calculations. It knows many conversion factors and constants, and mathematical functions (sin, cos, tan, ln, log, log2, exp, acos, atan and asin). It runs on the command line.

$ units -V units version 1.80 with readline, units database in /usr/share/units.dat $ grep Version /usr/share/units.dat
 * 1) 16 June 2002 Version 1.34

To specify temperatures in Celsius, write temp(C):

$ units -v 'tempC(25)' Definition: 298.15 K

To make ideal gas law calculations, specify R as the gas constant.

$ units -v R Definition: gasconstant = 8.314472 J / mol K = 8.314472 kg m^2 / K mol s^2

$ units -v '1 mol R tempC(0) / 1 atm' l 1 mol R tempC(0) / 1 atm = 22.413995 l 1 mol R tempC(0) / 1 atm = (1 / 0.044614983) l

Thermodynamic Properties of Propane
Some tables are available at [from http://www.care-refrigerants.co.uk/ a refrigerant vendor site].

Thermodynamic Properties of Water Vapor
Steam (water vapor) properties

Results from online steam tables:

This is what you input
 * temp 373.15 Degrees C

These are the results
 * The absolute pressure is: 218.58718889 bar
 * Specific volume of saturated liquid is: 2.53528848 cubic centimeters per gram
 * specific volume evap is: 1.46947084 cubic centimeters per gram
 * specific volume of saturated vapor is: 4.00475932 cubic centimeters per gram
 * enthalpy of saturated liquid is: 1979.50043200 Joules per gram
 * enthalpy evap is: 253.63983300 Joules per gram
 * enthalpy of saturated vapor is: 2233.14026500 Joules per gram
 * entropy of saturated liquid is: 4.24629652 kJ/kg K
 * entropy evap is: 0.39232409 kJ/kg K
 * entropy of saturated vapor is: 4.63897021 kJ/kg K

This is what you input
 * temp 26.85 Degrees C

These are the results
 * The absolute pressure is: 0.03533285 bar
 * Specific volume of saturated liquid is: 1.00339432 cubic centimeters per gram
 * specific volume evap is: 39146.28896400 cubic centimeters per gram
 * specific volume of saturated vapor is: 39146.28896400 cubic centimeters per gram
 * enthalpy of saturated liquid is: 112.50010684 Joules per gram
 * enthalpy evap is: 2438.15623100 Joules per gram
 * enthalpy of saturated vapor is: 2550.57181100 Joules per gram
 * entropy of saturated liquid is: 0.39276580 kJ/kg K
 * entropy evap is: 8.12692212 kJ/kg K
 * entropy of saturated vapor is: 8.52003752 kJ/kg K

This is what you input
 * temp 1.85 Degrees C

These are the results
 * The absolute pressure is: 0.00698352 bar
 * Specific volume of saturated liquid is: 1.00011747 cubic centimeters per gram
 * specific volume evap is: 181894.68440200 cubic centimeters per gram
 * specific volume of saturated vapor is: 181894.68440200 cubic centimeters per gram
 * enthalpy of saturated liquid is: 7.75483748 Joules per gram
 * enthalpy evap is: 2497.19825200 Joules per gram
 * enthalpy of saturated vapor is: 2504.94383200 Joules per gram
 * entropy of saturated liquid is: 0.02830277 kJ/kg K
 * entropy evap is: 9.08040930 kJ/kg K
 * entropy of saturated vapor is: 9.10857181 kJ/kg K

Some calculations:

 * Properties of a gigawatt

Mass of ball bearings
Volume of sphere is $$\frac43\pi r^3$$ $ units -v R Definition: gasconstant = 8.314472 J / mol K = 8.314472 kg m^2 / K mol s^2

$ units -v '1 mol R tempC(0) / 1 atm' l 1 mol R tempC(0) / 1 atm = 22.413995 l 1 mol R tempC(0) / 1 atm = (1 / 0.044614983) l

Thermodynamic Properties of Propane
Some tables are available at [from http://www.care-refrigerants.co.uk/ a refrigerant vendor site].

Thermodynamic Properties of Water Vapor
Steam (water vapor) properties

Results from online steam tables:

This is what you input
 * temp 373.15 Degrees C

These are the results
 * The absolute pressure is: 218.58718889 bar
 * Specific volume of saturated liquid is: 2.53528848 cubic centimeters per gram
 * specific volume evap is: 1.46947084 cubic centimeters per gram
 * specific volume of saturated vapor is: 4.00475932 cubic centimeters per gram
 * enthalpy of saturated liquid is: 1979.50043200 Joules per gram
 * enthalpy evap is: 253.63983300 Joules per gram
 * enthalpy of saturated vapor is: 2233.14026500 Joules per gram
 * entropy of saturated liquid is: 4.24629652 kJ/kg K
 * entropy evap is: 0.39232409 kJ/kg K
 * entropy of saturated vapor is: 4.63897021 kJ/kg K

This is what you input
 * temp 26.85 Degrees C

These are the results
 * The absolute pressure is: 0.03533285 bar
 * Specific volume of saturated liquid is: 1.00339432 cubic centimeters per gram
 * specific volume evap is: 39146.28896400 cubic centimeters per gram
 * specific volume of saturated vapor is: 39146.28896400 cubic centimeters per gram
 * enthalpy of saturated liquid is: 112.50010684 Joules per gram
 * enthalpy evap is: 2438.15623100 Joules per gram
 * enthalpy of saturated vapor is: 2550.57181100 Joules per gram
 * entropy of saturated liquid is: 0.39276580 kJ/kg K
 * entropy evap is: 8.12692212 kJ/kg K
 * entropy of saturated vapor is: 8.52003752 kJ/kg K

This is what you input
 * temp 1.85 Degrees C

These are the results
 * The absolute pressure is: 0.00698352 bar
 * Specific volume of saturated liquid is: 1.00011747 cubic centimeters per gram
 * specific volume evap is: 181894.68440200 cubic centimeters per gram
 * specific volume of saturated vapor is: 181894.68440200 cubic centimeters per gram
 * enthalpy of saturated liquid is: 7.75483748 Joules per gram
 * enthalpy evap is: 2497.19825200 Joules per gram
 * enthalpy of saturated vapor is: 2504.94383200 Joules per gram
 * entropy of saturated liquid is: 0.02830277 kJ/kg K
 * entropy evap is: 9.08040930 kJ/kg K
 * entropy of saturated vapor is: 9.10857181 kJ/kg K

Some calculations:

 * Properties of a gigawatt

Mass of ball bearings
$ units -v '(4/3) pi (1 inch)^3 7.86 g/cm^3' kg (4/3) pi (1 inch)^3 7.86 g/cm^3 = 0.53952591 kg
 * Volume of sphere is $$\frac43\pi r^3$$
 * Density of pure iron is $$7.86 \mathrm{g/cm}^3$$