What is Equilibrium: Definition and 1000 Discussions
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium there are no net macroscopic flows of matter or of energy, either within a system or between systems.
In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs.
Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, though not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium.
A thermodynamic system in a state of internal thermodynamic equilibrium has a spatially uniform temperature. Its intensive properties, other than temperature, may be driven to spatial inhomogeneity by an unchanging long-range force field imposed on it by its surroundings.
In systems that are at a state of non-equilibrium there are, by contrast, net flows of matter or energy. If such changes can be triggered to occur in a system in which they are not already occurring, the system is said to be in a meta-stable equilibrium.
Though not a widely named "law," it is an axiom of thermodynamics that there exist states of thermodynamic equilibrium. The second law of thermodynamics states that when a body of material starts from an equilibrium state, in which, portions of it are held at different states by more or less permeable or impermeable partitions, and a thermodynamic operation removes or makes the partitions more permeable and it is isolated, then it spontaneously reaches its own, new state of internal thermodynamic equilibrium, and this is accompanied by an increase in the sum of the entropies of the portions.
Homework Statement
http://imgur.com/yVOXkAT
The two disks each have a mass of 18kg and are attached at their centers by an elastic cord that has a stiffness of k = 1.6kN/m . Determine the stretch of the cord when the system is in equilibrium and the angle θ of the cord. (Figure 1)...
Homework Statement
An aqueous solution contains 0.84 g/L of an organic detergent. The osmotic pressure of this solution is 54.4 torr, at 25°C. What is the molar mass (in g/mol) of this detergent?
Homework Equations
##pi=MRT##
##R=0.08206L*atm/(mol*K)##
The Attempt at a Solution...
Can someone please help me with this one? I have found the equilibrium solutions,but I'm not sure what to do next.
Consider dx/dt = x^3 - 4x
Given a solution x(t) which satisfies the condition x(0) = 1, determine the limit(t -> infinity) of x(t).
Thanks!
Homework Statement
Find the equilibrium points of the system, determine their type and sketch the phase portrait.
##\frac{dx}{dt} = -3y + xy - 10, \frac{dy}{dt} = y^2 - x^2##
The attempt at a solution
Putting it together:
##\frac{dy}{dx} = \frac{y^2 - x^2}{-3y + xy - 10} \equiv...
Homework Statement
H2+CO2=CO+H2O
if 1.50 mol of each chemical species are placed in a 3.00l flask and allowed to achieve the equilibrium above, what mass of Co will be present at equilibrium?
Homework Equations
Keq= concentration of products each raised to the number of moles in...
Background:
I've derived the equation of motion of the bead shown in the picture below using the Lagrangian
\omega^2Rsin(\theta)+r\ddot{\theta}=0
The equilibrium points are at θ=0 and π. I'm now to show that only one of these points is stable.
Homework Statement
Show that only one of the...
What is the physical meaning of an object to be in stable equilibrium?
Would it make sense to say that the object wants to stay at that position and any movement will cause the restoring force to move the object back to equilibrium?
Homework Statement
in the attached picture are all the information needed to solve the problem.
The bent rod of a negligible weight is supported by a ball and a socket joint at A and a single journal bearing at B. End of D of the rod rests against a friction-less vertical surface. find...
Homework Statement
Trying to find angle u of bars (symmetrical) with ground at equilibrium under load.
Two bars, negligible weight of length .4m
Spring at midpoint k = 3kN/m, unstretched when bars at 45 deg
F = 150N, 5 deg
W of block 10kg
Slope of ground under block 5 deg
coef friction...
Hello,
I am wondering conceptually why the maximum conversion of products is made at chemical equilibrium? I was thinking if you use le chatelier to push towards products, the conversion will be higher.
Sorry if this sounds too vague, my prof's lecture was called "Equilibrium: The ultimate...
Homework Statement
The gas stream from a sulfur burner is composed of 15-mol% SO2, 20-mol% O2, and 65-mol% N2. This gas stream at 1 bar and 480 C enters a catalytic converter, where the SO2 is further oxidized to SO3. Find the equilibrium conversion of SO2. The equilibrium constant for...
Homework Statement
http://puu.sh/4NWw9.PNG
question 2.65**
Homework Equations
I've tried using the law of sine and law of cosine method with the triangle for equilibrium and I've tried the 600^2 = Fx^2 + Fy^2
The Attempt at a Solution
Here is what I did using the F^2 = Fx^2 + Fy^2...
Homework Statement
I need to find the tension T, γ and β in part 2 of this question.
The question is attached.
Homework Equations
First of all, the frame is a right angle triangle because (3L)^2 + (4L)^2 = (5L)^2
take torque about the point O
we got 2LF + mg(4Lcosγ) = Mg(3Lsinγ)
from...
A cylinder has rigid, adiabatic and impermeable external walls. It is provided with a mobile internal ideal partition wall, dividing it in two volumes (A and B). Each volume is filled with an ideal monoatomic gas. Initially, the volume, pressure and temperature of A and B are identical...
Hi!
I have problem with uderstanding of Liouville equation. Which sais that if we have a
Hamiltonian system (energy is conserved), then the the volume of phase space is
conserved, or equivalently the probability density is conserved (the total derivative
of probability density per time is...
This problem is trying to find out how much weight can be placed in the middle of a system before the weights on the outside go over the pulleys.
A diagram of the problem can be found here...
Homework Statement
For the reaction
2 NO_{2}(g) \leftrightarrow N_{2}O_{4}(g)
ΔH°_{rxn} = -57.2 kJ and ΔS°_{rxn} = -175.8 J/K
A 1 L container is initially filled with 1 atm of NO_{2} at 298 K. Find the equilibrium pressures of NO_{2} and N_{2}O_{4} at 298 K if
a. volume is held...
So in a given amount of solution, the equilibrium constant is the product of the concentrations of the ionic species present, raised to the power of the stoichiometric coefficient. Wouldn't it make more sense if it was the sum of the concentrations though,since basically the net number of ions...
My problem here is that I keep trying to make substitutions for the normal forces and cannot come up with the number for P. I saw 4.92 and don't understand how there is a range of force for which equilibrium can be maintained. The force I came up with for P is way too big, the answer is 0.955 lb
Homework Statement
What are the bifurcation values for the equation:
dy/dt = y^3 +ay^2
Homework Equations
The Attempt at a Solution
Equilibrium solutions:
y^3 + ay^2 = 0
==> y^2 (y + a) = 0
==> y = 0 (double root), or y = -a.
a = 0 is the sole bifurcation point, since...
Hello,
I want to make certain of my understanding of equilibrium solutions. Are equilibrium solutions the value(s) of y such that \frac{dy}{dt} = 0? So, suppose y = y0 is one of those solutions. Graphically, does this mean that one the horizontal line y = y0, little slope lines are too...
Homework Statement
Sum of downward forces exerted at A and B is 41lbs by the leg, what is the weight attached?
Homework Equations
None, really...
The Attempt at a Solution
Tension (T) throughout the system must be constant and equal to the weight (W).
I first assumed that the leg...
Problem Statement: As shown in the figure below, a uniform beam is supported by a cable at one end and the force of friction at the other end. The cable makes an angle of θ = 30°, the length of the beam is L = 1.50 m, the coefficient of static friction between the wall and the beam is μs =...
SOLVED
Homework Statement
A 23 kg child goes down a straight slide inclined 38∘ above horizontal. The child is acted on by his weight, the normal force from the slide, and kinetic friction. Find the magnitude of the normal force.
Homework Equations
cos(theta)=adjacent/hypotenuse
The...
I have a problem.
Lets say there were two pulleys put at equal height.
You have a metal ring and attach three wires to it.
At the end of each wire, have three weights of mass w.
One weight hangs down, one weight goes over one pulley and the other over the other pulley.
The system goes to...
Homework Statement
A sample of Mo-101, initially pure at time zero, beta decays to Tc-101 which then beta decays to Ru-101 (stable). The half-lives of Mo-101 and Tc-101 are nearly the same and for this problem are assumed equal (14.4 min). After a decay period of one half-life how many atoms...
It seems to me that change in permeability should not shift the equilibrium of entering and exiting ions, except how fast equilibrium is reached. Consider this: two compartments are separated by a membrane. 1st compartment holds 1mM Na+ and 10mM K+ and 2nd one holds 10mM Na+ and 1mM K+.
Let's...
So with this problem, I have been thinking about it. Since it is in equilibrium, I know the sum of forces and torques will be equal to zero. However, I'm not sure how the height, h, fits into this. I know the weights have a force and are a distance away from that fulcrum, d and 2d, so I could...
Homework Statement
transverse loads are applied to the beam in the figure at A, C, and E, and a concentrated couple 3Pa is applied to the beam at E. Determine expressions for (a) the transverse shear force Vc and bending moment Mc at a section just to the left of the load at C, and (b) shear...
Hello,
I am a first time poster and I need some help with a basic statics problem. I drew a free body diagram to help illustrate. An object with a mass 'M' is resting on a rotating disc that is spinning with constant velocity 'V'. The mass is continuously being pushed into a static wall due...
Law of cooling states that the rate of loss of heat by a body is directly proportional to the excess temperature of the body above that of its surroundings. The equation of determining temperature in time T(t)=Ta+(T0-Ta)*e^kt (Ta-ambient temperature, T0-initial temperature, k-heat transfer...
Homework Statement
As indicated in the diagram, consider a rail inclined at an angle θ relative to the horizontal axis. A sphere (A) with a charge +q is fixed at the bottom of the rail. A second sphere (B) with a charge +2q and a mass (m) is free to move along the rail. The sphere (C)...
I have a complicated 3d nonlinear differential system which I solve algebraically using maple's solve command. I aim to find the equilibrium points of the system using MAPLE and then plot these equilibrium points as a function of the 3 parameters alpha,beta,gamma(a.k.a.bifurcation diagram). The...
Homework Statement
Write the charge balance for a solution containing H(+), OH(-), Ca^(2+). HCO3(-). CO3^(2-) , Ca(HCO3)+, Ca(OH)+, K+, and CIO4(-).Homework Equations
Also, I am having a trouble understanding the concepts of mass balance and charge balance.
The Attempt at a Solution
The...
If I want to calculate the number of moles ratio of reactants which, in a reversible reaction of equilibrium constant K, will give me a certain yield 'f', what is the mathematical definition of the yield in this case?
For instance, in the reaction A + B ⇔ C + D, let's say we can denote extent...
Homework Statement
A conductor (wire) is folded into a square loop with each side having a length of a. Total charge of Q is transferred onto the conductor. Describe the line charge density of the square loop in equilibrium. (If I am interpreting this correctly what is required is...
Homework Statement
I.) Give an estimate for the stability constant of the complex [FeCl]2+, given that the standard redox potential for the Fe3+/Fe2+ system in 1 moldm-3 HCl is 0.710 V.
The "standard electrode potential of the reaction Fe3+ + e- -> Fe2+" (quote from the question) had...
Hi I have a 4 part question about phase changes and I hope you guys can help me out here thanks :)
The chemical equation for vaporization for water is H2O(l)-->H2O(g)
1) When ΔG is 0 during a phase change we would use the formula ΔH=TΔS and put in values to get the boiling/melting point by...
The problem statement
A uniform rod of length 2m and mass 5kg is connected to a vertical wall by a smooth hinge at A and a wire CB as shown. If a 10 Kg mass is attached to D, find:
a) the tension in the wire
b) the magnitude of the reaction at the hinge A.
attached is my copy of the...
Hi, I am currently studying Cosmology on my own, and I am learning about the Affleck-Dine mechanism of baryogenesis. I understand that in this case the baryon asymmetry is generated by the decay of a supersymmetric flat direction carrying B, which is excited during inflation.
Regarding...
Need help with equilibrium equations -- ASAP Please
Homework Statement
I'm studying for a final that I'm taking tomorrow and am stuck on the following:
Calculate Kc for the reaction:
4NOBr (g) \Leftrightarrow 4NO (g) + 2Br2 (g)
given the following information:
2NO(g) + Br2 (g)...
Two people are carrying a uniform wooden board that is 4.00 m long and weighs 180N. If one person applies an upward force equal to 80 N at one end, at what point does the other person lift?
m (distance from point of application of 80 N force)
I am thinking because of the the fact that...
Homework Statement
Description:
A ride consists of a carriage with a mass 300kg and with maximum occupancy of 300kg. The carriage is attached to a mechanical arm of length L = 5m that is capable of rotation. The arm is able to provide the torque necessary to swing the riders back and forth...
The equation ΔG=-nFEcell, I understand.
I also understand that, at unity activities of all species, Q=1 so R*T*ln(Q)=R*T*ln(1)=0. And therefore Ecell=E°cell and ΔG=ΔG°.
However, surely we cannot then write that ΔG°=-nFE°cell=-R*T*ln(K), since ΔG° is measured at unity activity when Q=1, rather...
I already have this equations. But I'm confused on how to solve it, because of this 100.
ΣFx=0
T₂Cos30°-T₃Cos60°-100N=0
ΣFy=0
T₂Sin30°+T₃Sin60°-9810N=0
How will I solve this? Please I Really have a problem on simplifying it, I need to solve for the T₂ and T₃
Homework Statement
If a beam with square cross-section and very low density is placed in water, it will turn one pair of its long opposite faces horizontal. This orientation,however, becomes unstable as we increase its density. Find the critical density when
this transition occurs. The...
1. Homework Statement [/b
A straight and homogenous stick with mass m is pressed against a wall with the force F. The stick is horizontal perpendicular against the wall. Given that the friction between the wall and the stick is μ, determine the horizontal component of F in order for the stick...