# What is Specific Volume

## What is Specific Volume

Specific volume is an intensive 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).

The density (ρ) of a substance is the reciprocal of its specific volume (ν).

ρ = m/V = 1/ρ

Density is defined as the mass per unit volume. It is also an intensive property, which is mathematically defined as mass divided by volume:

ρ = m/V

## Densest Materials on the Earth – Materials with Lowest Specific Volume

Since nucleons (protons and neutrons) 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. The densest material found on earth is the metal osmium, but its density pales by comparison to the densities of exotic astronomical objects such as white dwarf stars and neutron stars.

List of densest materials:

1. Osmium – 22.6 x 103 kg/m3
2. Iridium – 22.4 x 103 kg/m3
3. Platinum – 21.5 x 103 kg/m3
4. Rhenium – 21.0 x 103 kg/m3
5. Plutonium – 19.8 x 103 kg/m3
6. Gold – 19.3 x 103 kg/m3
7. Tungsten – 19.3 x 103 kg/m3
8. Uranium – 18.8 x 103 kg/m3
9. Tantalum – 16.6 x 103 kg/m3
10. Mercury – 13.6 x 103 kg/m3
11. Rhodium – 12.4 x 103 kg/m3
12. Thorium – 11.7 x 103 kg/m3
13. Lead – 11.3 x 103 kg/m3
14. Silver – 10.5 x 103 kg/m3

It must be noted, plutonium is a man-made isotope and is created from uranium in nuclear reactors. But, In fact, scientists have found trace amounts of naturally-occurring plutonium.

If we include man made elements, the densest so far is Hassium. Hassium is a chemical element with symbol Hs and 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 of 40.7 x 103 kg/m3.  The density of Hassium results from its high atomic weight and from the significant decrease in ionic radii of the elements in the lanthanide series, known as lanthanide and actinide contraction.

The density of Hassium is followed by Meitnerium (element 109, named after the physicist Lise Meitner), which has an estimated density of 37.4 x 103 kg/m3.

## Density of various Materials – Examples

Density of Water - Specific Volume
Pure water has its highest density 1000 kg/m3 at temperature 3.98oC (39.2oF). Water differs from most liquids in that it becomes less 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 therefore ice floats on 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 ().

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 Heavy Water
Pure heavy water (D2O) has a density about 11% greater than water, but is otherwise physically and chemically similar.

This difference is caused by the fact, the deuterium nucleus is twice as heavy as hydrogen nucleus. Since about 89% of the molecular weight of water comes from the single oxygen atom rather than the two hydrogen atoms, the weight of a heavy water molecule, is not substantially different from that of a normal water molecule. The molar mass of water is M(H2O) = 18.02 and the molar mass of heavy water is M(D2O) = 20.03 (each deuterium nucleus contains one neutron in contrast to hydrogen nucleus), therefore heavy water (D2O) has a density about 11% greater (20.03/18.03 = 1.112).

Pure heavy water (D2O) has its highest density 1106 kg/m3 at temperature 11.6oC (52.9oF). Also heavy water differs from most liquids in that it becomes less dense as it freezes. It has a maximum of density at 11.6oC (1106 kg/m3), whereas the density of its solid form ice is 1017 kg/m3. 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.

Density of Steam
Water and steam are a common medium because their properties are very well known. Their properties are tabulated in so called Steam Tables. In these tables the basic and key properties, such as pressure, temperature, enthalpy, density and 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 Steel
The density of steel varies based on the alloying constituents but usually ranges between 7.5 x 103 kg/m3 and 8 x 103 kg/m3.
Density of Zirconium
In general, zirconium has very low absorption cross-section of thermal neutrons, high hardness, ductility and corrosion resistance. One of the main uses of zirconium alloys is in nuclear technology, as cladding of fuel rods in nuclear reactors, due to its very low absorption cross-section (unlike the stainless steel). The density of typical zirconium alloy is about 6.6 x 103 kg/m3.
Density of Uranium
Uranium is a naturally-occurring chemical element with atomic number 92 which means there are 92 protons and 92 electrons in the atomic structure. Natural uranium consists primarily of isotope 238U (99.28%), therefore the atomic mass of uranium element is close to the atomic mass of 238U isotope (238.03u).  Natural uranium also consists of two other isotopes: 235U (0.71%) and 234U (0.0054%). Uranium has the highest atomic weight of the primordially occurring elements. Uranium metal has a very high density of 19.1 g/cm3, denser than lead (11.3 g/cm3), but slightly less dense than tungsten and gold (19.3 g/cm3).

Uranium metal is one of the densest materials found on earth:

1. Osmium – 22.6 x 103 kg/m3
2. Iridium – 22.4 x 103 kg/m3
3. Platinum – 21.5 x 103 kg/m3
4. Rhenium – 21.0 x 103 kg/m3
5. Plutonium – 19.8 x 103 kg/m3
6. Gold – 19.3 x 103 kg/m3
7. Tungsten – 19.3 x 103 kg/m3
8. Uranium – 18.8 x 103 kg/m3
9. Tantalum – 16.6 x 103 kg/m3
10. Mercury – 13.6 x 103 kg/m3
11. Rhodium – 12.4 x 103 kg/m3
12. Thorium – 11.7 x 103 kg/m3
13. Lead – 11.3 x 103 kg/m3
14. Silver – 10.5 x 103 kg/m3

But most of LWRs use the uranium fuel, which is in the form of uranium dioxide. Uranium dioxide is a black semiconducting solid with very low thermal conductivity. On the other hand the uranium dioxide has very high melting point and has well known behavior.

Uranium dioxide has significantly lower density than uranium in the metal form. Uranium dioxide has a density of 10.97 g/cm3, but this value may vary with fuel burnup, because at low burnup densification of pellets can occurs and at higher burnup swelling occurs.

References:
Reactor Physics and Thermal Hydraulics:
1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
5. Todreas Neil E., Kazimi Mujid S. Nuclear Systems Volume I: Thermal Hydraulic Fundamentals, Second Edition. CRC Press; 2 edition, 2012, ISBN: 978-0415802871
6. Zohuri B., McDaniel P. Thermodynamics in Nuclear Power Plant Systems. Springer; 2015, ISBN: 978-3-319-13419-2
7. Moran Michal J., Shapiro Howard N. Fundamentals of Engineering Thermodynamics, Fifth Edition, John Wiley & Sons, 2006, ISBN: 978-0-470-03037-0
8. Kleinstreuer C. Modern Fluid Dynamics. Springer, 2010, ISBN 978-1-4020-8670-0.
9. U.S. Department of Energy, THERMODYNAMICS, HEAT TRANSFER, AND FLUID FLOW. DOE Fundamentals Handbook, Volume 1, 2 and 3. June 1992.

## See above:

Thermodynamic Properties