What is Density
Densityis defined as themass per unit volume．It is anintensive property, which is mathematically defined as mass divided by volume:
ρ = m/V
In words, the density (ρ) of a substance is the total mass (m) of that substance divided by the total volume (V) occupied by that substance. The standard SI unit iskilograms per cubic meter(kg/m3). The Standard English unit ispounds mass per cubic foot(lbm/ft3). The density (ρ) of a substance is the reciprocal of itsspecific volume(ν).
ρ = m/V = 1/ρ
Specific volumeis anintensive variable, whereas volume is an extensive variable. The standard unit for specific volume in the SI system is cubic meters per kilogram (m3/kg). The standard unit in the English system is cubic feet per pound mass (ft3/lbm).
Theeffect of temperatureon the densities of liquids and solids is also very important. Most substancesexpand when heatedandcontract when cooled．However, the amount of expansion or contraction varies, depending on the material. This phenomenon is known asthermal expansion．The change in volume of a material which undergoes a temperature change is given by following relation:
where ∆T is the change in temperature, V is the original volume, ∆V is the change in volume, andαVis thecoefficient of volume expansion．
It must be noted, there are exceptions from this rule. For example,waterdiffers from most liquids in that it becomesless dense as it freezes．It has a maximum of density at 3.98 °C (1000 kg/m3), whereas the density of ice is 917 kg/m3．It differs by about 9% and thereforeice floatson liquid water
It is an illustrative example, following data do not correspond to any reactor design.
Pressurized water reactorsare cooled andmoderatedby high-pressure liquid water (e.g. 16MPa).At this pressure water boils at approximately 350°C (662°F). Inlet temperature of the water is about 290°C (⍴ ~ 720 kg/m3). The water (coolant) is heated in thereactor coreto approximately 325°C (⍴ ~ 654 kg/m3) as the water flows through the core.
The primary circuit of typical PWRs is divided into 4 independent loops (piping diameter ~ 700mm), each loop comprises asteam generatorand onemain coolant pump．Inside the reactor pressure vessel (RPV), the coolant first flows down outside the reactor core (through the downcomer). From the bottom of the pressure vessel, the flow is reversed up through the core, where thecoolant temperature increasesas it passes through the fuel rods and the assemblies formed by them.
Calculate:
- Pressure loss due to thecoolant accelerationin an isolated fuel channel
when
- channel inletflow velocity is equal to 5.17 m/s
- channel outletflow velocity is equal to 5.69 m/s
Solution:
The pressure loss due to the coolant acceleration in an isolated fuel channel is then:
This fact has important consequences. Due to the different relative power of fuel assemblies in a core, these fuel assemblies havedifferent hydraulic resistanceand this may induce local lateral flow of primary coolant and it must be considered in thermal-hydraulic calculations.
Densest Materials on the Earth
Sincenucleons(protonsandneutrons) make up most of the mass of ordinary atoms, the density of normal matter tends to be limited by how closely we can pack these nucleons and depends on the internal atomic structure of a substance. Thedensest materialfound on earth is themetal osmium, but its density pales by comparison to the densities of exotic astronomical objects such as whitedwarf starsandneutron stars．
List of densest materials:
- Osmium – 22.6 x 103kg/m3
- Iridium – 22.4 x 103kg/m3
- Platinum – 21.5 x 103kg/m3
- Rhenium – 21.0 x 103kg/m3
- Plutonium – 19.8 x 103kg/m3
- 金- 19.3 x 103kg/m3
- Tungsten – 19.3 x 103kg/m3
- Uranium – 18.8 x 103kg/m3
- Tantalum – 16.6 x 103kg/m3
- Mercury – 13.6 x 103kg/m3
- Rhodium – 12.4 x 103kg/m3
- Thorium – 11.7 x 103kg/m3
- Lead – 11.3 x 103kg/m3
- Silver – 10.5 x 103kg/m3
It must be noted, plutonium is a man-made isotope and is created fromuraniuminnuclear reactors．But, In fact, scientists have found trace amounts of naturally-occurring plutonium.
If we include man made elements, the densest so far isHassium．Hassiumis a chemical element with symbolHsand atomic number 108. It is a synthetic element (first synthesised at Hasse in Germany) and radioactive. The most stable known isotope,269Hs, has a half-life of approximately 9.7 seconds. It has an estimated density of40.7 x 103kg/m3．The density of Hassium results from itshigh atomic weightand from the significant decrease inionic radiiof the elements in the lanthanide series, known aslanthanide and actinide contraction．
The density of Hassium is followed byMeitnerium(element 109, named after the physicist Lise Meitner), which has an estimated density of37.4 x 103kg/m3．
Density of various Materials – Examples
Pure water has its highest density1000 kg/m3at temperature3.98o
C(39.2
o
F).Water differs from most liquids in that it becomesless dense as it freezes．It has a maximum of density at 3.98 °C (1000 kg/m3), whereas the density of ice is 917 kg/m3．It differs by about 9% and thereforeice floatson liquid water. It must be noted, the change in density is not linear with temperature, because the volumetric thermal expansion coefficient for water is not constant over the temperature range. The density of water (1 gram per cubic centimetre) was originally used to define the gram. The density (⍴) of a substance is the reciprocal of its specific volume (ν).ρ = m/V = 1/ν
具体的体积(ν)的一种物质是完全的l volume (V) of that substance divided by the total mass (m) of that substance (volume per unit mass). It has units of cubic meter per kilogram (m3/kg).
Water and steam are a common medium because their properties are verywell known．Their properties are tabulated in so called“
Steam Tables
”．In these tables the basic and key properties, such as pressure, temperature, enthalpy,densityand specific heat, are tabulated along the vapor-liquid saturation curve as a function of both temperature and pressure.The density (⍴) of any substance is the reciprocal of its specific volume ().
ρ = m/V = 1/
The specific volume () of a substance is the total volume (V) of that substance divided by the total mass (m) of that substance (volume per unit mass). It has units of cubic meter per kilogram (m3/kg).
Density of Nuclear Matter
Nuclear densityis the density of the nucleus of an atom. It is the ratio of mass per unit volume inside the nucleus. Since atomic nucleus carries most of atom’s mass and atomic nucleus is very small in comparison to entire atom, the nuclear density is very high.
The nuclear density for a typical nucleus can be approximately calculated from the size of the nucleus and from its mass.Typicalnuclear radiiare of the order10−14m．Assuming spherical shape, nuclear radii can be calculated according to following formula:
r = r0．A1/3
where r0= 1.2 x 10-15m = 1.2 fm
For example,natural uraniumconsists primarily of isotope238U(99.28%), therefore the atomic mass of uranium element is close to the atomic mass of238U isotope (238.03u). Its radius of this nucleus will be:
r = r0．A1/3= 7.44 fm.
Assuming it is spherical, its volume will be:
V = 4πr3/3 = 1.73 x 10-42m3．
The usual definition of nuclear density gives for its density:
ρnucleus= m / V = 238 x 1.66 x 10-27/ (1.73 x 10-42) =2.3 x 1017kg/m3．
Thus, the density of nuclear material is more than 2.1014times greater than that of water. It is an immense density. The descriptive termnuclear density也适用于类似的情况下高吗densities occur, such as within neutron stars. Such immense densities are also found in neutron stars.
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