# Density Mass Volume

## What is Mass and Weight

The mass of an object is a fundamental property of the object. It is a numerical measure of its inertia and the measure of an object’s resistance to acceleration when a force is applied. It is also a fundamental measure of the amount of matter in the object. The greater the mass, the greater the force needed to cause a given acceleration. This is reflected in Newton’s second law (F=ma).

The mass of a certain body will remain constant even if the gravitational acceleration acting upon that body changes. For example, on earth an object has a certain mass and a certain weight. When the same object is placed in outer space, away from the earth’s gravitational field, its mass remains the same, but it is now in a “weightless” condition. This means in this condition it will weight zero, because gravitational acceleration and, thus, force will equal to zero.

Mass and weight are related: Bodies having large mass also have large weight. A large stone is hard to throw because of its large mass, and hard to lift off the ground because of its large weight. To understand the relationship between mass and weight, consider a freely falling stone, that has an acceleration of magnitude g (g = 9.81 m/s2 is the acceleration due to Earth’s gravitational field). Newton’s second law tells us that a force must act to produce this acceleration. If a 1 kilogram stone falls with an acceleration of the required force has magnitude:

F = ma = 1 [kg] x 9.81 [m/s2] = 9.8 [kg m/s2] = 9.8 N

## What is Density

Density is defined as the mass per unit volume. It is an intensive 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 is kilograms per cubic meter (kg/m3). The Standard English unit is pounds mass per cubic foot (lbm/ft3). The density (ρ) of a substance is the reciprocal of its specific volume (ν).

ρ = m/V = 1/ρ

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).

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.

Density