Thermodynamics Definition and 1000 Threads

Hi all, I have a question. So from the derivation of the Isentropic process relationship PV^gamma = constant, there is a step dW = PdV, which can only be said for quasi-equilibrium (or reversible) processes. As such I believe PV^gamma = constant (and the family of equations) should not be...

I am currently undertaking a research internship where I am modelling the heating of silicon wafers with a 515 nm femtosecond laser. In order to increase the absorption of the laser into the oxide layer on top of the wafer it was suggested we use gold nanoparticles. I was tasked with modelling...

Hello, I have been studying nuclear magnetic physics, focusing on phenomena such as nuclear magnetic resonance (NMR), and I started wondering whether there is any relationship with the famous Maxwell's demon thought experiment. Maxwell's demon is a conceptual idea often discussed in the context...

IMO, this problem is really tricky. Here below is my attempt. Let us take a perfectly insulated container and imagine dividing it with an alternating series of walls: those with an odd index are rigid and conduct heat, bringing the two adjacent compartments into thermal contact; those with an...

Jacobson’s work (1995) [1] demonstrated that Einstein’s equations can be derived from thermodynamic principles, suggesting gravity might emerge from the thermodynamic behavior of spacetime, tied to the entropy of horizons. Other researchers, such as Bekenstein [2] and Verlinde [3], have explored...

Hello, I've been struggling with understanding how the molar fraction term appears in the expression of chemical potential as a fonction of pressure when the element is in a mixture, here is the proof given in my textbook for the expression of chemical potential of a pure substance (pure gas)...

I’m repeating a simple freezing experiment using commercial plastic mineral water. The bottles contain pre-formed, macroscopic gas bubbles that remain perfectly spherical and adhered to the inner wall of the plastic. When these bottles are sealed, freezing often preserves the bubbles intact...

I performed a simple test: First, I briefly opened and closed a plastic mineral water bottle to allow air exchange. Then I left it untouched at room temperature for about half an hour, until multiple gas bubbles formed inside. After that, I placed the bottle in the freezer. What caught my...

While boiling water in a standard stainless steel milk jug (open top, approx. 10 cm diameter), I happened to notice two intriguing phenomena under simple and reproducible conditions. • Approx. 400 ml of filtered water was used. • Heat was applied via direct flame until a continuous...

For the first part, I got the answer pretty easily, it is a well known fact that the change in the entropy of the system does not matter about the process taken, so its the same for both reversible and irreversible processes, i.e nR ln(Vf/Vi). To derive this, I have assumed that the temperature...

I found the specific volume to be 0.2 m^3/kg (0.1 / 0.5), this gives me a dryness fraction (x) of 0.4311 Then I can use Q = m(h2 - h1) h2 is just enthalpy for superheated steam at 400kPa and 300 Celsius = 3066.8 kJ/kg but for h1 do I now use: h = hf + (x.hfg) or do I use h = x.hg + (1-x).hf I...

I tried to use Taylor expansion to see what would happen to the equation, but I kept having problems with the term (hν/kT)² Have a nice day, everyone!

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...

Hi all, any thoughts on the following problem please? When saturated steam is expanded isentropically across a turbine, the dryness fraction should decrease. However, when I calculated the answer to the following question, it actually increased slightly. Any ideas where I went wrong? Question...

So basically I've seen that in Persia as well as in other areas, people have been using ice pools and other means to produce ice in the desert. Specifically ice pools used the fact that deserts have low humidity, as this would mean higher evaporative cooling efficiency as well as radiative...

As I'm studying for my PE and taking practice exams, I came across several problems where the solution assumes that a steam turbine is isentropic. I am now all confused and questioning my knowledge up to this point. It says in the problem statement that the turbine is "80% efficient". If that is...

a) To try to solve this problem I used the Clausius-Clapeyron equation $$\ln{\frac{P_2}{P_1}}=-\frac{\Delta H^\circ_{vap}}{R}\left (\frac{1}{T_2}-\frac{1}{T_1}\right )$$ with ##P_2=253\ \text{Torr}##, ##P_1=35\ \text{Torr}##, ##T_2=189.55\text{K}##, and ##T_1=161.2\text{K}##. I obtained...

Before we prove this, consider a thought experiment. We have the following setup We break the left partition so that the gases on the left mix. What happens next is that due to a chemical potential difference, gas flows from the right compartment to the mixture. Note that - the partial...

I've attached all my work and data table I used to answer the questions but there isn't an answer key so I would like a second opinion. a) The initial specific internal energy is.......Btu/lbm b) The initial mass is....lbm c)The average enthalpy of the withdrawn vapor is.....Btu/lbm d)The final...

I have been thinking this for quite a few time. At this point we know that our universe is going through an accelerated expansion phase. I was also doing some work on blackhole thermodynamics, specially P-V criticality, heat capacity, Joule Thomson expansion, heat engine etc. These...

Hello, all, I am currently trying to solve a problem at my internship concerning the heat transfer analysis of a Grade-2 titanium rod. The Ti rod is placed in an environment of 300 degrees C, and I am trying to solve the problem of the steady-state temperature of the Ti capsule. The length of...

In thermodynamics we tend to think of pressure as the frequency of collisions with the walls of the container. And we say that the more the collisions the higher the pressure, the less the collisions the lower the pressure. So lets say we have an ideal monoatomic gas enclosed in a cube...

My approach to the problem was to try using Q = cmΔt by rearranging it to solve for Δt=Q/cm. Since the power per person is 70 W, there are 1800 people in the concert hall, and the problem asks for the temperature rise over two hours, I multiplied 70 W×1800 people × (3600 sec × 2) which gave me...

In *An Introduction to Thermal Physics* by Schroeder, while deriving the multiplicity of an ideal gas makes the following statements (image below): Even in quantum mechanics, the number of allowed wavefunctions is infinite. But the number of independent wavefunctions (in a technical sense...

Okay, so the first law ##dU=dQ+dW##. We all know that ##dU=C_VdT##. So that means that we have: $$dQ=C_VdT+PdV$$ Now I have a problem. We also have that $$dU=\left(\frac{\partial U}{\partial V}\right)_TdV+\left(\frac{\partial U}{\partial T}\right)_VdT$$ and substituting that in to ##dQ=dU+dW##...

I met a paradox I am unable to resolve. Here it goes: a special material is placed in thermal contact with 2 reservoirs kept at different temperature. The boundaries of the material that aren't in contact with the reservoirs are thermally insulated. The material being special is able to generate...

Okay, so we have that $$dU = \left( \frac{\partial U}{\partial V} \right)_S dV + \left( \frac{\partial U}{\partial S} \right)_V dS$$ And comparing that to the first law, we get that $$T=\left(\frac{\partial U}{\partial S}\right)_V$$. Comparing expressions of ##T##...

I'm 64. My background prior to 2001 - Aviation, experimental aircraft and aerodynamics, robotics, mechanical and software engineering, disaster recovery. Since 2001 - Human sustainability and global recovery, researching every related sector in depth in order to understand what can now be proven...

My professor said that F is not additive, meaning F ≠ F1 + F2, where F1 is the helmholtz energy of system 1 and F2 is the helmholtz energy of system 2. So my question is, how can I decide wether a thermodynamic potential (F, H, G) is additive or not?

Okay, I agree with this logic. However, if we consider a reversible section first, then an irreversible section, I get the following: $$\frac{dQ_{rev}}{T} \leq \frac{dQ}{T} $$ which is the opposite to equation (14.8). Why is this? Is it "somehow" not viable to think of a reversible section than...

and the solutions: I am not sure why two of the bodies are at the same temperature to end with. I am pretty certain that they don't have to be - but the author of the problem set it this way for some reason I'm missing (my guess). My reasoning: Put 100 K and 300 K together for a short time...

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...

I have a recipe that was a scratch cake of my grandmothers, but it is made for a ## 9 ~\text{in} \times 13 ~\text{in} ## baking pan. I wish to bake three ## 9 ~\text{in} ## rounds from the recipe. I can look up baking times online for the size, but times are dependent somewhat on the recipe...

I am not convinced that the heat entering ##T_l## from ##T_h## is equal to ##Q_l## in the Carnot engine. Why should it be? thanks

Ideal gas: If the gases are of different type, I would say the entropy stays the same. The total entropy is in both cases just the sum S = S1 + S2, where S1 is the entropy of the first gas and S2 the entropy of the second gas. If the gases are of the same type, I think the entropy change is also...

I get that the relative fluctuations of extensive properties (in thermodynamics) are tiny because you can divide the whole system in many subsystems and apply the central limit theorem, but I just dont get it with intensive properties. Could someone explain?

I've seen this math also in a lecture once. It seems very vague to me. Here is the relevant part of the book ##F_1## and ##F_2## are introduced as seen above. There is, as far as I can tell, no previous mention of them. Why does ##F_1(P_A,V_A,P_B,V_B)=0## signify thermal equilibrium...

I study Aerodynamics & Thermodynamics for my own pleasure, and am especially devoting my time now to civil aircraft design, in all its forms. I mainly learned from John Anderson and Jack Mattingly wonderful books. Thank you.

This is chemistry but it's basically physics :D. I used PV = nRT, I get V = 37.44 L. This is fine. So then I have W = P(Vfinal - Vinitial). Vinitial is zero, because there was no hydrogen gas initially. So I get 3.78 kJ. And as the gas expanded from 0 L to 37.44 L, the gas has done positive...

I was looking at the proof of zeroth law of thermodynamics from the original paper by Bardeen, Carter, Hawking, which can be found here. Now, we have the Killing vector which is the generator of the horizon, we call it ##l^\mu##, and auxiliary null vector field ##n^\mu##, which we define to be...

Since the energy variation is zero: $$ \Delta U = \Delta U_{1} + \Delta U_{2} = 0 $$ The energy for a monatomic ideal gas is ## u = CRT##, and the energy for a Van der Waals gas is $$ u = CRT - \frac{a}{v}, $$ obtained through $$ \frac{1}{T} = \frac{CR}{a + \frac{a}{v}}. $$ Summing the...

I am attempting to derive equations of state for a flow loop that incorporates a magnetohydrodynamic (MHD) generator to extract energy from the working fluid, an ionized gas. I have been able to find the following equation to define the power output of the generator: (where K is load factor, σ...

Then $$q_{irrev}=0\tag{1}$$ Take the system from state 2 back to state 1 using a reversible process B. My first question is: why can the system not be isolated for this reversible process to be possible? Assume we have a non-isolated system in process B. Process A and process B together...

When I was taught about temperature in high school, I was told that substances that are hot have molecules that move fast, while substances that are cold have molecules that move slowly. I was also told that everything moves towards greater disorder or entropy. This is apparently because there...

First, I thought of the forces which are acting upon the piston. F1 + G = F2, where F1 = p1 * S and F2 = p2 * S p1 + mg/S = p2 I figured that before and after the gas' temperature rises, the piston has to be at equilibrium, so p2 - p1 = p2' - p1'. p1V1 = niu * R * T1 p2V2 = niu * R * T1 =>...

In, *An Introduction to Thermal Physics, page 235*, Schroder wants to evaluate the partition function $$Z_{tot}=\sum_0^\infty (2j+1)e^{-j(j+1)\epsilon/kT}$$ in the limit that $kT\gg\epsilon$, thus he writes $$Z_{tot}\approx\int_0^\infty (2j+1)e^{-j(j+1)\epsilon/kT}\,dj$$ But how is this...

If a process is irreversible, on the other hand, then $$\oint \frac{\delta q}{T}\leq 0=\oint dS\tag{1}$$ Apparently, from this equation we can conclude that $$dS \geq \frac{\delta q}{T}\tag{2}$$ How do we mathematically justify the step from (1) to (2)? Next, consider an isolated system...

After re-reading the book, I did figure out what I was supposed to do. Take both waters through a series of reservoirs to bring them down to their final temperature while allowing for a quasi-static process. Thus, $$\Delta S = m_1c \int_{T_1}^{T*} \frac{dT}{T} + m_2c \int_{T_2}^{T*}...

When we remove the stoppers, the gas expands and the piston shoots up and eventually reaches a new final position in which the internal and external pressures are the same. Apparently we can write $$\delta q=0\tag{1}$$ $$\delta w=-P_2dV\tag{2}$$ $$dU=C_VdT\tag{3}$$ $$dU=-P_2dV\tag{4}$$...

For the internal energy function ##U(S,V,\{n_i\})## we have $$dU=TdS-pdV+\sum\limits_{i=1}^{N_s}\mu_id n_i\tag{1}$$ where ##N_s## is the number of species in the system. We also have $$dU=\delta q+\delta w\tag{2}$$ by the 1st law of thermodynamics. I am using ##\delta## to denote an inexact...