What is Mass conservation: Definition and 22 Discussions

In physics and chemistry, the law of conservation of mass or principle of mass conservation states that for any system closed to all transfers of matter and energy, the mass of the system must remain constant over time, as the system's mass cannot change, so quantity can neither be added nor be removed. Therefore, the quantity of mass is conserved over time.
The law implies that mass can neither be created nor destroyed, although it may be rearranged in space, or the entities associated with it may be changed in form. For example, in chemical reactions, the mass of the chemical components before the reaction is equal to the mass of the components after the reaction. Thus, during any chemical reaction and low-energy thermodynamic processes in an isolated system, the total mass of the reactants, or starting materials, must be equal to the mass of the products.
The concept of mass conservation is widely used in many fields such as chemistry, mechanics, and fluid dynamics. Historically, mass conservation was demonstrated in chemical reactions independently by Mikhail Lomonosov and later rediscovered by Antoine Lavoisier in the late 18th century. The formulation of this law was of crucial importance in the progress from alchemy to the modern natural science of chemistry.
The conservation of mass only holds approximately and is considered part of a series of assumptions coming from classical mechanics. The law has to be modified to comply with the laws of quantum mechanics and special relativity under the principle of mass-energy equivalence, which states that energy and mass form one conserved quantity. For very energetic systems the conservation of mass-only is shown not to hold, as is the case in nuclear reactions and particle-antiparticle annihilation in particle physics.
Mass is also not generally conserved in open systems. Such is the case when various forms of energy and matter are allowed into, or out of, the system. However, unless radioactivity or nuclear reactions are involved, the amount of energy escaping (or entering) such systems as heat, mechanical work, or electromagnetic radiation is usually too small to be measured as a decrease (or increase) in the mass of the system.
For systems where large gravitational fields are involved, general relativity has to be taken into account, where mass-energy conservation becomes a more complex concept, subject to different definitions, and neither mass nor energy is as strictly and simply conserved as is the case in special relativity.

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  1. S

    How to convert to the number of sand and Nylon particles from mass

    I calculate 4.8x10(^10) particles /kg of sand in the sample. Do you find the same ? Is my solution correct ? How many particles do you find ? Thanks in advance !
  2. Feynstein100

    I Does mass conservation correspond to a pseudo-symmetry?

    Emmy Nöther proved that mathematically, if a certain quantity is conserved, there must be a corresponding symmetry somewhere. Momentum conservation stems from spatial symmetry, charge conservation stems from complex phase symmetry at the quantum level and energy conservation stems from time...
  3. Andrew1235

    Mass conservation in a sphere to find radial velocity of a flame

    I am not sure what form of mass conservation to use to solve the above problem from An Introduction to Combustion by Stephen Turns. Can anyone explain what form of mass conservation applies to a sphere in this context?
  4. George26

    Conservation of mass: control volume approach question

    Summary:: Control volume question that has a brine solution entering a tank and mass accumulates over time. Hello, I'm currently struggling with a control volume approach question that has a brine solution entering a tank. I get to a point where I have a first order differential equation. I...
  5. WhiteWolf98

    Fluid Dynamics - Mass Conservation, State Equation for an Ideal Gas

    I understand that ##\dot m=\rho Q## and ##{\dot m}_{in}= {\dot m}_{out}## . So one can say that ##\rho Q_1 = \rho Q_2##. But I'm not sure if that equation is correct. I don't know if the density remains constant, or the volume flow rate. And then how I'm also supposed to tie a state equation in...
  6. H

    Diffusion down chemical potential gradients

    Ignoring cross-diffusion, diffusive mass fluxes down chemical potential gradients can be described by the equation (I am working from de Groot and Mazur's 1984 text on non-equilibrium thermodynamics): \frac{\partial C_k}{\partial t} = L_{kk}\frac{\partial (\mu_k-\mu_n)}{\partial x} where C_k...
  7. daPope

    Have mass flow rate, want superficial vapour velocity

    Hi guys, quick simple question. Lets say I have a pipe separated into 3 sectoins (all horizontal), all have the same flow areas. In the first section it is all liquid water. I know the mass flow rate in this. In the second section the water is heated. And I can work out the steam quality...
  8. J

    Is the concept of finite mass-energy in the universe outdated?

    I've always understood that there's a fnite amount of mass energy in the universe, please correct me if this view is out of date. As a particle accelerates it's mass increases how does this square with not being able to create mass or energy?
  9. WannabeNewton

    Mass conservation charged dust

    Hi guys! This is related to a recent thread but since that thread became cluttered, I figured it would be more coherent to just ask the question here. Say we have a congruence of charged dust particles in some space-time with tangent field ##\xi^a##. The energy-momentum of the charged dust is...
  10. E

    Mass conservation for pulsating sphere

    Hi, I'm trying to understand the mass conservation equation for a pulsating sphere which has thickness dr. Please refer to the attached solution. \rho = \rho_{0} (ambient density) + \rho' (small deviation) There are two things I don't follow. First, is that to obtain the mass, the area of...
  11. L

    Mass Conservation and Reynold Transport theorem for Non Uniform flow

    Homework Statement I will honestly be so grateful if someone can explain this to me. I am studying the Reynolds transport theorem, particularly mass conservation. I have read over my notes and I really do not understand how to calculate the mass flow rate through the control surface if it...
  12. S

    Solving Mass Conservation with Characteristic System

    Hello i want to solve \frac{\partial \rho}{\partial t}=\frac{\partial v_1\rho}{\partial x_1}+\frac{\partial v_2\rho}{\partial x_2} for v_1 = -x_2 and v_2=x_1 i obtain equation \frac{\partial \rho}{\partial t}+x_2\frac{\partial\rho}{\partial x_1}-x_1\frac{\partial \rho}{\partial...
  13. S

    Mass conservation in a conical tank

    Good Morning to all I saw this problem in one of the courses that I am taking this semester. It is very simple, it consists of an open conical tank being filled in the upper part with an stream (which is assumed to be cylindrical) of water (flow Qi through an area Ai). At the bottom of the...
  14. T

    General relativity question on mass conservation integral

    Homework Statement Starting off with a general axisymmetric metric: ds^{2}=g_{tt}dt^{2}+2g_{t\phi }dtd\phi + g_{\phi \phi }d\phi^{2} +g_{rr}dr^2 + g_{\theta \theta }d\theta ^2...\left ( 1 \right ) where the metric components are functions of r and theta only. I have deduced (using...
  15. T

    Deriving the mass conservation integral in GR

    Homework Statement Starting from a general axisymmetric metric ds^2=g_tt dt^2 + 2g_tφ dtdφ +g_φφ dφ^2 + g_rr dr^2+g_θθ dθ^2 ...(0) where the metric components are functions of the coordinates r and θ only. I've managed to show (via Euler-Lagrange equations) that g_tt dt/dτ + g_tφ...
  16. N

    Mass conservation in radially symmetric parabolic PDE problems

    Dear all, I'm trying to solve the 2d heat equation in a radially symmetric domain, numerically using the Crank-Nicolson method. i.e. \dfrac{\partial u}{\partial t} = D\left( \dfrac{\partial^2u}{\partial r^2}+\dfrac{1}{r}\dfrac{\partial u}{\partial r}\right) Applying the Crank-Nicolson...
  17. G

    Combustion mass conservation integral

    Homework Statement integrate [(rs^2)*(rhos)*(us)*(db/dr)=(d/dr)*(r^2)*(rho)*(D)*(db/dr))] rs=radius at surface rhos=density at surface us=velocity at surface r = radius rho = density D= diffusivity b=spalding non-dimensional parameter Homework Equations The Attempt at a...
  18. W

    Mass Conservation in Chemical Reactions

    I realize that to calculate heat being released and contained during nuclear reaction you must understand the difference between its product mass and reactant mass by using *E=mc2.* My Question pertains to the heat being released during a chemical reaction... Is Mass conserved in this chemical...
  19. R

    Mass conservation in fluid mechanics

    Part of the mechanics course I'm taking this semester are also fluids, but the material our teacher gave us to this topic is very poor (but unfortunately I haven't found a better source). The problem is that there are many "magic formulas", which come just out of nowhere - without any...
  20. N

    How Do You Calculate Mass Flow Rate on an Inclined Plane?

    so i got this HW prob, and i don't know exactly where to start, Oil flows steadily in a thin layer down an inclined plane. The velocity profile is u = [(density)(g)(sin theta) / Mu] [(hy - (0.5)y^2] express the mass flow rate per unit width in terms of density, Mu, g, theta, and h...
  21. Reshma

    Mass conservation in meson theory

    In the Meson theory of nuclear forces, exchange of pi meson is given by: n\rightarrow n + \pi^{0} p\rightarrow p + \pi^{0} n\rightarrow p + \pi^{-} p\rightarrow n + \pi^{+} Here the charge is conserved. But I don't understand how mass conservation takes place as in some of the cases a...
  22. R

    Beta-Plus Decay: Exploring Mass Conservation

    Hello all, In beta-plus decay, a proton decays into a neutron and emmits a positron. If the neutron weighs more than the proton where did the extra mass come from?