Equilibrium Definition and 1000 Threads

Consider an adiabatic container divided into two chambers by a movable, heat-conducting wall. One side contains a monatomic ideal gas, while the other contains a diatomic ideal gas. Initially, both gases are at the same temperature and pressure. Over time, the wall moves until a new...

So if I understand correctly the forces acting on the sphere are ##\vec{F}##, the normal force, friction, and the weight of the sphere. In order for the conditions of static equilibrium to be met the net torque must be zero. The torque about the center of the sphere created by the normal...

(My attempt of drawing the forces is the figure with the arrows). Intuitively I would say that non of the rods are supported in any of these configurations, but I struggle to give a good explanation for why. I could guess that B would be able to keep up, however summing the forces, it seems just...

Why can't we use the Boltzmann distribution to calculate what fraction of particles are in the liquid and gas states? If in liquid state the potential energy is smaller by amount ##L## per mole lets say, the using the Boltzmann distribution (##r\propto \exp(-\Delta E/RT)##) the fraction of...

From the van't Hoff equation we have $$\ln{\left ( \frac{K_p(T_1)}{K_p(T_2)} \right )}=\frac{\Delta H^\circ_{rxn}}{R}\left ( \frac{1}{T_2}-\frac{1}{T_1} \right )\tag{1}$$ So for ##T_2>T_1## we have ##K_p(T_1)<K_p(T_2)##. which is to say that the equilibrium constant increases for the higher...

Suppose we have the following balanced equation $$\nu_A A+\nu_B B\rightleftharpoons \nu_C C+\nu_D D,\ \ \ \ \ \Delta G^\circ_{rxn}$$ At equilibrium we have $$Q_{eq}=K_P=\frac{P_C^{\nu_C}P_D^{\nu_D}}{P_A^{\nu_A}P_B^{\nu_B}}=e^{-\Delta G_{rxn}^\circ/RT}$$ What I think I am confused about is...

We have that ##\Delta G = -RT\ln K##. This is in my lecture notes. However, it does not specify whether ##K## is ##K_c## or ##K_p##. Fair enough, I assumed that it could be both. However, when writing out the definitions of ##K_p## and ##K_c##, and using the fact that ##P=CRT##, where ##C## is...

The solution given is as following: Consider an arbitrary set of charges in equilibrium, and imagine moving them out to infinity by uniformly expanding the size of the configuration, so that all relative distances stay the same. For example, in part (b) we will simply expand the equilateral...

We start with ##n_i## moles of phosgene and zero of the products. The initial total pressure and also partial pressure of phosgene is ##\frac{n_iRT}{V}##. At equilibrium, suppose ##x## moles of phosgene have reacted. Then we have ##n_i-x## moles of phosgene left and ##x## mole of each of the...

Hi, apart from the interesting wording of this question, I'm struggling to understand the concept of what we need to do here. I started by having three equations (summation Fx, summation Fy and Moment about Y). I also calculated the two reaction forces about A and the one rection force about B...

Dear all, I have the following problem: I need to find the compression "C" in the mast and the angle that the masts makes with the horizontal (X degrees). I know that the tension in the ropes "T" are of the same magnitude on both sides of the pulley, but I am struggling with finding C and X...

For this problem, I took the moment about point B to 'get rid' of the tension force in the cables BA and BC. By doing this, I figured I could solve for the x and y components of the reaction force at D. From there, I could solve for the tension in BA and BC in the x and y and then solve for Dz...

The time scale on which the change (such as a change in external parameters or a external parameters or an addition of heat) takes place is referred to as τ_exp. The relaxation time τ_relax, on the other hand, is the time that the system needs to return to a state of equilibrium after a sudden...

Consider a structure comprising an elastic deformable body (in pink) attached to a rigid body (in yellow) at the right side ( $\Gamma_c$ interface) and fixed at the left side. Assume a force $F$ is applied to the rigid body at an angle $\beta$, as shown in the diagram. Subsequently, the...

It’s usually being assumed that points of equilibrium liquid – its vapor is given by a curve in the (P,T) coordinates, and this curve doesn’t change no matter is there another gas in the system or not. For example: if water is put in the empty volume, it will obviously vaporize, filling the...

Consider the differential equation ## \ddot{x}+cos(x)=0 ##. Note that ## \ddot{x}=f(x, \dot{x}) ##, so we have ## f(x, y)=-cos(x) ##. Then ## f(x, 0)=-cos(x)=0 ##. This gives ## x=n\pi-\frac{\pi}{2} ## for some ## n\in\mathbb{Z} ##. Since the differential equation for the phase paths is given by...

Cooling Lerasium to its melting point: Q1 =m L⋅c L,liquid ⋅(T L,i −T L,melt) Q1 = 1.49kg⋅221.6J/kgK⋅(1108.1−56.4)K Q1 = 330.184 ⋅(1051.7) = 347254.512 J Heating Atium to its melting point: Q2 =mA⋅cA,solid ⋅(TA,melt −TA,i) Q2 = 2.44kg⋅524.8J/kgK⋅(308−33.6)K Q2 = 1280.512⋅(274.4) = 351372.493 J...

In the formula above I have that the mechanical momentum of the horizontal force with respect to ##C## is always ##0## because the point of application coincides with the pole. Also, the mechanical momentum of the costraint reactions is ##0## because the costraint is smooth so the reaction is...

I hope this is more properly laid out? We previously established that the stationery points were (1,1) and (-1,1) For this first stage I now need to create the elements of a Jacobian maitrix using partial differentation. I am confused by reference to the chain rule. Am I correct that for dx/dt...

my question is short simply why reversibility requires equilibrium?

I use ##l-1## lagrangian coordinates ##\alpha_1,...,\alpha_{l-1}## . ##\alpha_i## is the angle between ##OP_{i-1}## and ##OP_{i}##. As the length of a chord between two rays with angle ##\alpha## is ##d=2Rsin(\alpha/2)##, I write the potential energy of the system as...

For this problem I set ΣFy = -3kN - 0.75kN - 3kN + Ay + By (with By representing the right side vertical force, and Ay representing the left side force). For ΣM, I used the rectangular distributed load of 0.5 kN at 3m from point A as the pivot: ΣM = -3m*Ay - (0.5kN*4m) - 3kN*6m - 5kN*m + By*6m...

I think the first part is F = mxa? But given the jib is resting on a turntable at a certain distance, does that mean the longer and shorted ends experience different loads? Especially when the shorter end has a 16T counterweight? The second part, I have no idea how to calculate this nor the...

I do know how to solve this question: We find the equilibrium pressure due to air molecules inside the container (after water has stopped flowing). Then, assuming initial pressure of gas inside the container to be atmospheric pressure, we use Boyle's law to find the new volume of the gas and...

Can someone explain that, when using the formula (Fs=1/2 kx^2) why do we use x=0.1m instead of 0.05m? Seems like a simple concept but why isn't it 0.05m (since 0.05m from equilibrium). Thanks.

I know that if 2 systems A and B are in equilibrium their coordinates doesn't change. Systems are not complicated and be fully described using two separated coordinates X and Y. What will happen if I seprate them using an adiabatic wall? Their coordinates start to change but I cannot...

Hi, I have this pulley question, i have to find the force F that needs to be applied to the string to keep the system in equilibrium. I found 150N. Is it correct? T_1= 300N and T_2=150N so F is 150N.

The problem is based on a similar thread. In fact, the first question is extremely similar. However, the second question is the one I consider more interesting but I posted the first one too for context. If this was just 1 pulley and two masses, then equilibrium is only possible if both masses...

Please can one explain what is exactly gonna happen if we have closed container and liquid is present in it and we heat from bottom ? Then whole liquid will converted into vapour or not ? But during the phase change both system in dynamic equilibrium. If both phases are in dynamic equilibrium...

Let a = distance between the charge on the left to the third bead. Since the electric field is equilibrium, we equate the electric field emanating from the left charge to the right charge at the location of the third bead. I want to try to find the ratio of d with a. E=E Kq/(d-a)^2 = K*3q/a^2...

I am only interested in the initial equilibrium conditions, and I am struggling to convince myself whether that should correspond to the equality of chemical potentials for H2 or an equality of temperatures as well. My work is as below: We take both gases as simple ideal (this is only relevant...

Question: Suppose that two bodies of masses m1 and m2 are a fixed distance d apart, and that both of them act on a third body of mass m. Find the position of the third body such that the two forces are in equilibrium. I have solved this question and obtained the answer listed in the back of the...

I'm able to get the force of the top spring (6.75N upwards) by setting the sum of all forces equal to 0 as everything is stationary. Where I'm stuck is starting the second part of the problem. I initially tried setting the sum of torques equal to 0 using the top spring as a lever arm but unless...

Suppose we put benzoic acid in a buffered solution at pH=2. In this condition, it will be almost completely unionized and therefore not very soluble. Conversely, if it is placed in a basic environment, the solubility will be high. But why does this happen? Is there a shift in the acid...

I've come across a puzzling thought experiment. Consider two black bodies surrounded by vacuum. The surrounding temperature is exactly 0 K. By some ingenious optical device all the radiation from body 1 is focused onto body 2 and vice versa. If left alone sufficiently long the two bodies will...

For this problem, I don't understand why this is impossible. Can someone please help? Many thanks!

In the d(i) part, we are asked to write an equilibrium constant. It was mentioned in the chapter that solids and liquids will not be added in the equation. So, I think that there is not going to be any Expression for this reaction as all the reactants and products are liquids. Is my answer right?

The equation for indicator is: HIn ⇌H+ + In- Which reaction (forward or reverse) will be preferred when I increase the Alkali. According to me, The reverse reaction should be preferred as the reaction will try to minimize the effect of the change. Hence In- (i.e the conjugate base) will be...

In the coursebook the question says: The reaction below was carried out at a pressure of 10×10⁴ Pa and at constant temperature. N2 + O2 ⇌ 2NO the partial pressures of Nitrogen and Oxygen are both 4.85×10⁴ pa  Ccalculate the partial pressure of the nitrogen(ll) oxide, NO(g) at equilibrium. In...

In screenshot below, systems A and B are separated by an adiabatic wall initially while each of them exchanges energy with system C via a diathermic wall. Once A and B reach thermal equilibrium with C, then A,B are allowed energy exchange via a diathermic wall, and energy exchange between A and...

During a recent visit to the Modern Museum of Art in Fort Worth I came across this remarkable sculpture. It appears to be free standing (no strings attached). I assumed it is screwed into the floor and, for obvious reasons, I didn't poke it to see if it will tip over. My thinking is that the...

My thermodynamics is rusty and my current endeavors demand me to wield it, so here we go: I need a good starting point and/or references to study physical systems in thermodynamic equilibrium. Any references which address the fluid mechanics perspective of said systems are welcome too. Let me...

Hi... i want to draw Equilibrium curve for SO2 oxidation to SO3, i found following relations but don't know to use them... kindly tell me how to draw Equilibrium curve using these equations or any source on web from where i can get directly SO2 oxidation data Vs Temp? Equations are following...

Figure: My attempt at a solution: For the calculation of ##F_{DB}## we consider the equilibrium in the whole machine. $$\left. \begin{array}{r} h\rightarrow h=6\cdot \sin \theta +3=6,44\, \textrm{ft} \\ d\rightarrow d=6\cos \theta -1,5=3,41\, \textrm{ft} \end{array}\right\} \,\, \alpha =\arctan...

Figure: My attempt at a Solution: We calculate REACTIONS: $$\sum F_x=0\rightarrow \boxed{Bx=0}\qquad \sum F_y=0\rightarrow By+A=50$$ $$\sum M_B=0\rightarrow \boxed{A=25\, \textrm{kN}}\quad \boxed{B=25\, \textrm{kN}}$$ KNOT B: $$\alpha \rightarrow \alpha =90-40=50\, \textrm{º}$$ $$\beta...

Figure: Attempt at a Solution: $$F=k\Delta x=lk\sin \theta$$ $$\delta x=0 \quad \textrm{when} \theta=0$$ $$\sum M_C=0\rightarrow$$ $$\rightarrow Pl\cos \theta -F_yl\cos \theta -F_xl\sin \theta =0\rightarrow$$ $$\rightarrow Pl\cos \theta -Fl\cos^2 \theta -Fl\sin^2 \theta=0\rightarrow$$...

SO2(g)+1/2O2(g)⇌SO3(g);ΔHo=-98.32KJ/mole,ΔSo=-95J/(mole-K). find Kp at 298 Kelvin? In given question at first Δ G will be calculated using formula ΔG = Δ H – T x ΔS, by putting the given values in formula we get ΔG = -70.01 kJ/mol. Then Keq will be calculated using equation = Δ G = -RT ln Keq...