What is Conservation of mass: Definition and 55 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. E

    I Conservation of Mass for Compressible Flow

    I'm trying to figure out how the mathematics of conservation of mass in compressible flow works for a simple setup. I posted this problem in hw physics section, and the conversation turned to the physics model and appears to have gone kaput. This was supposed to be a mathematics question (but...
  2. H

    A Boundary conditions for variable length bar

    Suppose I'm looking at a bar of length L(t) in 1D and I have the conservation of mass: \frac{\partial\rho}{\partial t}+\frac{\partial}{\partial x}(\rho u)=0 In order to make things easier, I make the change of variable x'=x/L(t) so that in this frame of reference, the length remains constant...
  3. M

    The direction of flux vectors in derivation of conservation of mass

    In the derivation of the conservation law of the conservation of mass, the flux on one side enters and the flux on the other side leaves the control volume. I presume this is due to the assumption that the volume is infinitesimally small and hence v(x,y,z,t) will not change directions...
  4. S

    I Special Theory of Relativity & Conservation of Mass

    Does the law of conservation of mass fail to meet the first postulate of the special theory of relativity(the laws of physics are the same in all inertial frames of reference)?
  5. 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...
  6. JGHunter

    Lavoisier's Law of conservation of mass

    Hi, I'm writing a short story which addresses an issue in time travel that I don't really see getting addressed, and I was wondering where I could find the original quote where it is written that mass or energy can neither be created nor destroyed? I'm aware the original won't be in English...
  7. 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...
  8. T

    Fluid mechanics: Bernoulli's equation and conservation of mass

    Homework Statement A mechanical servo-mechanism comprising of a movable piston-cylinder within a vertical cylinder operates based on a venturi contraction in a horizontal 350mm diameter pipe that delivers a fluid of relative density 0.95. The upper end of the 100mm diameter vertical cylinder is...
  9. Nick tringali

    Is the Law of Conservation of Mass Always Obeyed?

    Are the laws of conservation of mass always obeyed. in a nuclear reaction mass is converted to energy therefore mass isn't conserved. I understand that energy is always conserved, but I feel like mass isn't.
  10. M

    Fluids: Continuity and Conservation of Mass

    Hi PF! In fluids I've noticed many authors use the continuity equation with an integral form of conservation of volume (assume density is constant). Is this double counting? Example: let fluid velocity inside an idle bubble be ##\vec u = \nabla \phi##. Conservation of mass implies ##\nabla u =...
  11. Undacuva

    Underpinnings of conservation of energy/mass

    I understand the 1st law of thermodynamics developed as a generalization based on experimental observations, in that an exception has yet to be found in thousands of situations, so it is considered to hold true in all possible situations. If that is how it developed, is there any other theory or...
  12. M

    Conservation of Mass Fluids Wave

    Hi PF! Suppose we have a water wave with mean depth ##H## with disturbance ##\zeta## above/below ##H## propagating through a channel of thickness ##b##. The book parenthetically remarks that the continuity equation becomes $$\partial_t(b(H+\zeta))+\partial_x(bHu)=0.$$ However, when I try...
  13. M

    Conservation of mass relation for a closed system

    Source: Çengel/Cimbala. Above part is confusing for me from some points. First of it what can a closed system refer to? I just understand a piston/cylinder arrangement with an ideal gas in it. But this concept must be more comprehensive than I have it in my mind. Second, does "closed system...
  14. N

    Are Exothermic Reactions a Violation of the Law of Conservation of Mass?

    Are exothermic reactions violation of law of conservation of mass , because energy and mass are equivalent? Please clarify!
  15. parshyaa

    How can we prove the law of conservation of mass

    How can we prove the law of conservation of mass ? I said prove not the verification, how lavoiser decided that yes this law is followed by every chemical reaction, is there a proof
  16. Z

    I Is mass conserved in relativistic collision?

    For a particle , E2 = (pc)2 + (moc2)2 and for a system of particle , (ΣE)2 = (Σpc)2 + (Σmoc2)2 so in that way before a collision, (ΣEi)2 = (Σpic)2 + (Σmoic2)2 and after , (ΣEf)2 = (Σpfc)2 + (Σmofc2)2 and as far as i know energy and momentum is conserved . so that means ΣEi=ΣEf and also Σpi=Σpf...
  17. M

    Why Use Time Derivative Outside the Integral in the Continuity Equation?

    Hi PF! Can someone help me understand why, when writing the continuity equation we write: $$\frac{\partial}{\partial t} \iiint_v \rho \, dv$$ instead of $$ \iiint_v \frac{\partial}{\partial t} \rho \, dv$$ I understand the two are not necessarily the same, but why derive it the first way...
  18. denisaf

    Laws of Mass Dynamics: Conservation & Transformation

    The laws of thermodynamics deal with the irreversible flow of energy. Conservation of energy is the first law and increasing entropy (disorder) in an energy flow is the second. The conservation of mass is the equivalent first law for matter. It is commonly recognized. But what about the...
  19. MCarsten

    Solid rocket velocity and distance

    Hi there. I'm new to the forum. I apologize if I'm posting at the wrong session. Anyway, here goes the problem: (sorry for any grammar typos). A solid fuel rocket, home constructed, has initial mass 10 kg; this, fuel is 8 kg. The rocket is launched vertically, from rest; burning the fuel at a...
  20. S

    Matter/antimatter annihilation and conservation of mass

    I was hoping to learn a little bit more about matter-antimatter annihilation. As I understand it, when a particle meets an antiparticle, they are both annihilated and energy is produced. Does this contradict the laws of conservation of energy and conservation of matter? I haven't had much luck...
  21. N

    Mutual Induction and Law of Conservation of Mass

    In mutual induction, when a coil is turned on or off, it generates voltage in another nearby coil. But where is that voltage coming from? It can't be created, so what form of energy does it convert from? As far as I know, when the magnetic field cuts across the coil, that generates voltage...
  22. L

    Does Conservation of Mass Make This "Health Study" Invalid?

    This is a study that was published in the New England Journal of Medicine done on the safety of e-cigs or better known as vaping. The article states, "They found that vaping 3 milligrams of e-cigarette liquid at a high voltage can generate 14 milligrams of loosely affiliated or "hidden"...
  23. T

    Torque, Angular Momentum, and Conservation of Mass Problems

    Homework Statement I am studying the topics listed above and have been having great difficulty getting my problems going. To explain, I am having difficulty seeing where the problem should go and attacking in that direction. I can draw out free-body diagrams but I can't see how to solve the...
  24. soulmartyr

    Conservation of mass and black holes

    With this post I am hoping someone would be kind enough to lead me in the right direction. I am a layman who knows little about the actual math behind physics, nonetheless I have developed an interest in it and wish to expand my knowledge base. First question I have is if someone could...
  25. 1

    Conservation of mass incongruent with He?

    Hi physicists! My name is grant and I am curious as to how helium plays into our Earth's overall mass and gravity. It's my understanding that gravity itself is functionally dependent on the quantity of mass within closed systems or objects, and it's also my understanding that helium will...
  26. M

    The conservation of mass in a region enclosing flow

    Homework Statement In the equation representing the conservation of mass enclosing flow: \int\rho \underline{u} \cdot \underline{\widetilde{n}} dA = 0 where: \underline{u}= velocity vector \underline{\widetilde{n}} = unit vector normal to surface A a) what the meaning of the term...
  27. N

    Conservation of mass and energy

    Hmm, I s matter always conserved? Is mass always conserved? Is rest-mass always conserved? Is energy always conserved? are there any exceptions?
  28. R

    Conservation of Mass Principle applied to Refrigerators

    Dear all, Can the conservation of mass principle be applied to the mass flow rate of a refrigerant in an ideal refrigerator system? And what about for an actual refrigeration system? I'm reading the principle here but can't work it out. Says that it applies for steady flow, but I assume...
  29. shounakbhatta

    Conservation of mass - Stellar equation

    Conservation of mass -- Stellar equation Hello, I was reading over a article on hydrostatic equilibrium of stars. I came across a chapter stating Conservation of Mass, where there is a sphere: r distance from the sphere, density as a function of radius ρ(r). Let m be the mass interior to r...
  30. T

    Fluid flow through a pipe - Conservation of mass and/or momentum?

    Homework Statement The Attempt at a Solution So first I found the density of the air coming in and going out. Next I used conservation of momentum with two forces caused by the pressures at the entrance and the exit of the nozzle. I end up getting 1004 which is not the same as...
  31. T

    Fluid mechanics - Conservation of mass problem

    Homework Statement Here is the question along with my attempt: As you see in my second equation there are two unknowns, A_out and dm/dt. I think my problem is that I don't exactly understand the equation. dm/dt is the net mass flow rate. For example if dm/dt is a positive number then there...
  32. B

    How Do You Calculate the Speed of a Bungee Jumper 19m Below the Launch Point?

    Homework Statement A bungee jumper of mass 75 kg is standing on a platform 53m above the river. The length of the unstretched bungee cord is 11m. The spring constant of the cord is 65.5N/m. Calculate the jumpers speed at 19m below the bridge on the first fall. Homework Equations Em1=Em2...
  33. S

    Interpreting Data to Satisfy Conservation of Mass

    Homework Statement This is not homework. I am having trouble interpreting this data. I don't see how it satisfies a conservation of mass. As the temperature is increasing, how is acetone increasing its mole fraction in both phases? If the mole fraction of acetone increases in one phase...
  34. R

    Conservation of Mass of Air Flowing in Duct

    Homework Statement The problem asks, air at 20 degrees celsius enters a 2-m long closed channel with 5mm x 5mm square duct at 0.2 m/s. One part of the question asks, if someone clams that the average velocity of the exiting air is slightly more than 0.2m/s, does this violate the conservation...
  35. R

    Does Conservation of Mass Apply to Compressible Gases in Vents?

    Hi Just a quick question about Conservation of Mass that I somehow managed to confuse myself: If I have a vent of constant cross section at steady state, given that conservation of mass means that inlet and exit mass flow rate must be the same, does this mean that, taking the...
  36. N

    Centripetal force with Conservation of Mass

    1. Homework Statement : Essentially it is a loop with a ramp leading to it. Find the height h the car would start from in order to complete the loop. Also find the speed the car would have to be at to complete the loop Your answer should be in terms of r. No friction 2. Homework Equations : I...
  37. P

    Applying conservation of mass to a falling plywood

    A sheet of plywood is held with one edge resting on the floor, as shown in the figure below. The plywood surface initially makes a small angle, Θ, to the floor. At time t=0 the held edge is released and the plywood pivots about the edge on the floor as it falls down. It is observed that the...
  38. V

    Proton=positron+neutron. what about law of conservation of mass?

    neutron weighs higher than proton and you add a mass of positron which is around equal to to electron. so mass in right had side is much larger than that is LHS so is it disobeying Law of conservation of mass? if it disobeys it and follow law of conservation of mass and energy.(E=mc2) then it...
  39. T

    Β+ decay: voiding conservation of mass or creating something with negative mass

    From Wikipedia: "Positron emission or beta plus decay (β+ decay) is a type of beta decay in which a proton is converted, via the weak force, to a neutron, releasing a positron (the antimatter counterpart of an electron) and a neutrino. Isotopes which undergo this decay and thereby emit...
  40. P

    Wormhole - Conservation of Mass

    I'm going to apologize now if what I say doesn't really make sense, I'm still only learning the basics of physics. Let's say that few hundred or maybe thousands of years, we developed some sort of device that can rip a hole into the space time fabric to create a wormhole. If a spaceship...
  41. S

    Does the Law of Conservation of Mass Apply to Annihilation of Matter?

    If the law of conservation of mass states, in a closed system mass is never lost, how is it, when matter is annihilated, effectively creating photons (which are not considered to be matter) does this law stand true?
  42. A

    Laws of conservation of mass (roller coaster) work and mechanical energy

    Homework Statement A 4.0 x 10^4kg roller coaster starts from rest at point A. Neglecting Friction, calculate its potential eneregy relative to the ground, its kinetic energy, and it's speed at points, B, C, and D. at point A : 54m B: 15m c:47m d:35mHomework Equations i got potential eneregy by...
  43. L

    Law of conservation of mass question

    " In a chemical reaction matter can be neither created nor destroyed " So does this law only apply to chemical reactions or can matter ever be destroyed or created in any way shape or form? and do people believe that something that has been burned can be unburned? It says that when...
  44. C

    Conservation of Mass: Is It True?

    Simple question: Rest Frame: In their respective rest frames, the following objects have the following rest masses: Object A Mass = 1 kg ; Object B Mass = 1 kg. Total Rest Mass of system: 2 kg. A & B accelerate and reach some constant Velocity. At this velocity, their relative masses are...
  45. J

    Conservation of Mass - Does Burning Wood Convert Mass to Energy?

    My chem teacher told me once that if you could gather all the atoms produced after burning a piece of wood, you would have the same amount of mass you started with. Is this true, or does some of it get converted to energy? I'm reading about "Pair Production and Annihilation", and the...
  46. Y

    Understanding the Law of Conservation of Mass: Mathematical and Verbal Proofs

    Homework Statement The conservation of Mass states that the total mass of substances is the same before and after a chemical or physical change occurs. Explain why this is true in yet not true of density. Explanations to include mathematical as well as verbal proofs. The Attempt at a...
  47. A

    Deriving Conservation of Mass & Momentum for an Inviscid Compressible Gas

    Homework Statement Starting from the equations of conservation of mass and momentum for an inviscid compressible gas, \frac{\partial \rho}{\partial t} + \bigtriangledown . (\rho {\bf u}) = 0 \rho ( \frac{\partial {\bf u}}{\partial t} + ({\bf u}. \bigtriangledown){\bf u}) = \bigtriangledown...
  48. G

    Calculating Density of Vapor After Heating 3-Liter Vessel

    Any help is greatly appreciated, A 3-liter vessel contains 2kg of water, 0.05kmol of steam, and 15cm3 of ice (density = 990kg/m3). If the vessel is heated until its entire contents have vaporized, what is the density of the vapor? now i know I've to use M(in) - M(out) = M(vessel). If...
  49. Q

    Why Water Decreases in Cross-Sxn Area: Conservation of Mass

    Why does water bottleneck or decrease in cross sectional area when it falls from the faucet. The book says it is conservation of mass stuff... (Cross-Sxn Area)* (velocity) = constant. How can that be if all the water is accelerating at the same pace. What I mean is that all the water...