In thermodynamics, an adiabatic process (from the Greek adiábatos, meaning “impassable”) is a type of thermodynamic process which occurs without transferring heat or mass between the system and its surroundings. Unlike an isothermal process, an adiabatic process transfers energy to the surroundings only as work. It also conceptually supports the theory used to explain the first law of thermodynamics and is therefore a key thermodynamic concept.
Some chemical and physical processes occur too rapidly for energy to enter or leave the system as heat, allowing a convenient "adiabatic approximation". For example, the adiabatic flame temperature uses this approximation to calculate the upper limit of flame temperature by assuming combustion loses no heat to its surroundings.
In meteorology and oceanography, adiabatic cooling produces condensation of moisture or salinity, oversaturating the parcel. Therefore, the excess must be removed. There, the process becomes a pseudo-adiabatic process whereby the liquid water or salt that condenses is assumed to be removed upon formation by idealized instantaneous precipitation. The pseudoadiabatic process is only defined for expansion because a compressed parcel becomes warmer and remains undersaturated.
TL;DR Summary: Problem said that the ball moves in a harmonic motion and asked to prove it. The process is adiabatic
Problem said that the ball moves in a harmonic motion and asked to prove it. The process is adiabatic.
I did the development, but at certain point I'm having a problem. The...
I was trying to solve a JEE ADVANCED 2020 paper 1 question 13 on thermodynamics. I attempted the problem and got a different answer than they did. I did it in a different way, but I can't find a mistake in both methods. So now I am stuck. I think the problem is in the first step probably using...
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...
In case of adiabatic process, we all know that the relation between temperature and pressure and that's given below:
P. T(γ/(1-γ)) = Const.
therefore, P = Const. T(γ/(γ - 1))
or, ΔP = Const. (γ/(γ - 1)).ΔT(1/(γ - 1))
It's just an attempt to find out the relation. Don't know how much correct I...
I was unable show that ##PV^k## must indeed equal some function of the entropy, ##g(S)##; maybe doing so would make things easier? I proceeded as below.
If we assume (as is almost surely intended by Callen) that in the given adiabatic (##d Q = 0##) process we are taking ##N## as constant and...
Using the adiabatic process formula, I've calculated the change in volume for a volume of gas with an initial pressure of 10 psig expanding to 0 psig. The initial volume is 100 cubic inches and the expanded volume is 144.9. This is a difference of 44.9. The total work done ends up being about...
Hello! If I have a 2 level system, with the energy splitting between the 2 levels ##\omega_{12}## and an external perturbation characterized by a frequency ##\omega_P##, if ##\omega_{12}>>\omega_P## I can use the adiabatic approximation, and assume that the initial state of the system changes...
Hello! Assume I have a 2 level system, where the 2 levels have opposite parity. If I apply an electric field, I will get an induced dipole moment. For now I want to keep it general, so the induced dipole moment can be very large, too. Let's say that I start rotating this electric field in the...
(picture of diagram below)So the task goes like this: gas is ideal. Process 3->1 s adiabatic and in process 1->2 work done is 1200J. Fill the table.
I don't know how to calculate work done in an adiabatic process because p2 and V2 are not given and I don't know gama(Cp/Cv).
I know that deltaU...
The first law of Thermodynamics states that the change in Internal energy is equal to the sum of Heat gained or lost by the system and work done by the system or on the system .
$dE=Q-W$...(1).
In an Adiabatic process ,Q=0 .
Therefore $dE=-W$ .
Now...
The equation I know for adiabatic work is W = P1V1((V1/V2)ϒ-1 - 1))/ϒ-1, but this involves ϒ, but I can use ϒ = Cp/Cv = Cv+R/Cv = 1 + Cv/R, does this seem correct? But I still have a P1
The statement does not say whether the process is reversible or not, but I suppose the only way to solve the problem is by thinking it actually is.
I tried using the formula for reversible adiabatic processes, i.e. PVγ = constant. First, I calculated the initial volume with the ideal gas law...
I have attached an image showing the perimeters of the problem.
I have included what I think is the solution, could someone please take a look and tell me if I am on the correct path, in the solution I am taking Joules as a common term to attempt to solve the question. The gas I have used is N...
I took the w derivative of the wave function and got the following. Also w is a function of time, I just didn't notate it for brevity:
$$-\frac{\sqrt{2}n\pi x}{w^{3/2}}cos(\frac{n\pi}{w}x) - \frac{1}{\sqrt{2w^3}}sin^2(\frac{n\pi}{w}x)$$
Then I multiplied the complex conjugate of the wave...
Im confused on working backwards so to speak to find adiabatic work.
To find work for this adiabatic process, I either need to know the change in temperature OR the initial pressure (I think?).
The issue is that I don't know either the initial temperature nor the initial pressure so I am not...
In this problem, the method used to solve the question is to equate pdV with change in internal energy. This implies an adiabatic process as Q = 0? (not sure about this claim) However, why is it not correct to simply apply the PV^ϒ = constant formula?
Thank you.
I have been able to get everything except entropy. I know it's not zero. I know I have to find a reversible path to calculate it, but keep coming up with strange values so I don't think I'm doing it correctly.
can I do CpdT/T + CvdT/T = ds? I am having trouble calculating my P2 (I know my final...
Hi all,
For an Isothermal compression process of air in a vessel with constant volume, I found the following expressions
and
and
The first two give the same result, meanwhile the third gives another solution and I don't know why.
For adiabatic compression I found these two expression which...
in this textbook : http://www.fulviofrisone.com/attachments/article/486/Huang,%20Kerson%20-%201987%20-%20Statistical%20Mechanics%202Ed%20(Wiley)(T)(506S).pdf ;page 20
I don't understand about Eq 1.11 come to 1.12 ? I know
dU = U_V dT + U_T dV
dQ = dU + p dV
put dU into dQ. So dQ = U_V dT...
I tried by one way, seems ok and makes sense, but i am not sure if it is valid yet.
$$P_{a} = c_{a}V_{a}^{(-\gamma_{a})}$$
$$P_{b} = c_{b}V_{b}^{(-\gamma_{b})}$$
$$(Pa,va = Pb,vb)$$
$$\frac{c_{a}}{c_{b}} =\frac{[V_{b}^{-\gamma_{b}}]}{[V_{a}^{-\gamma_{a}}]} = V^{-\gamma_{b}+\gamma{a}}$$
Now this...
Hi,
A quick question on a conundrum I seem to have encountered. My main question is: why is it wrong to use the formula above instead of the SFEE approach?
My approach:
Use the formula:
$$ w = \frac{R}{1-n} (T_2 - T_1) $$
From the data book, ## R = 0.287 ## kJ/kg K and ## n = \gamma = 1.4 ##...
I was puzzling over how to solve this and finally peeked at the solution. They used the relevant equation above.
I disagree with this though. The problem specifically says “the piston is allowed to slide freely!” This means that we don’t let it happen slowly. So then we are not in...
My question is: Do ALL the reversible process need to be composed of ONLY isothermal and adiabatic transformations? Carnot cycle satisfy this, but what other cycle would be also reversible?
I know that for a process to be reverisble it has to be almost-static, have no dissipative force, and no...
Here is what I did :
work done in going from A to C,
W1 = 2nRToln(2) (isothermal process)
work done in going from C to B,
W1 = pΔV = nRΔT = -nRTo (isobaric process)
work done in going from B to A,
W3 = 0 (isochoric process)
so, total work done = W1 + W2 + W3...
1.
Adiabatic compression (When compressed quickly, there is no heat flow to the environment Q=0)
Isochoric with heat loss (The syringe is still compressed, there should be no change in volume)
Adiabatic expansion (When the syringe is released, there is work done only)
Isochoric with heat gain...
This is a relatively simple problem, but I'm not getting the right answer. For adiabatic compression, work on gas is positive, since work on gas = ΔEth and the adiabatic process moves from a lower isotherm to a higher one. Integrating for work gives:
pV * (Vf(1 - gamma) - Vi(1 -...
For compressible flow in a duct, mass conservation combined with reversibility (no entropy change) implies $$(1-\frac{u^2}{c^2})\frac{du}{u} = -\frac{dA}{A}$$
where u is the flow velocity of the gas, c is the speed of sound in the gas, and A is the area of the duct. I am assuming a calorically...
I'm not sure that this is an adiabatic process. As far as i can read, it is adiabatic if no HEAT or ENERGY is added. But pumping in molecules that are a non-zero temperature is an addition of energy, no?
Anyway - my solution with the assumption of an adiabatic process.
(skipping units for...
I verified with others the equation below is an Euler method as well with ##a## can be any value such that it give the same ##\frac{dE}{dv}=-1.4\frac{p}{v}## but with ##a## other than one, it have no meaning in physics. For anyone that already understand Euler method can omit the part i have...
I tried this question and this the answer given in the book.
A cylinder is close at both ends and has insulating walls. It is divided into two compartments by a perfectly insulating partition that is perpendicular to the axis of the cylinder. Each compartment contains 1.00 mol of oxygen, which...
The actual data for the problem and my (and my friend's) attempt at a solution are in the attached file.
In a nutshell, this is what happened.
I obtained a solution based on the fact that the system is isolated. Thus the initially hot gas moves the partition doing work onto the initially cold...
The speed of sound in a gas at temperature T is given to be ## v=\sqrt{\frac{\gamma RT}{M}}##, where ##\gamma## is the adiabatic exponent, R is the gas constant and M is the molar mass of the gas. In deriving this expression, we assumed that the compression and expansion processes were so fast...
How is to possible to change the temperature without exchange of heat?
Could you please give me an example?
I know it is possible to keep the temperature constant while there is exchange of heat. This is possible when the heat supplied is consumed/lost to the surrounding.
But how is it...
(i) In this case the gas is expanding therefore its volume will increase and the pressure will drop. As volume gets bigger particles have more space to move around.
Isobaric is curve (1-2). It’s a horizontal line because here the pressure is constant.
Isothermal is curve (1-3) temp is constant...
Homework Statement: An adiabatic pendulum (right) is coupled via a spring with spring contant κ to a normal non-variable pendulum. The pendula have equal mass m and, initially, equal length l . The right pendulum is adiabatically pulled up with frequency ω(t)
1. Derive the equations of motion...
Why is a thermally isolated process that occurs sufficiently slow is necessarily adiabatic and not just reversible process ? Here I mean that the definition of adiabatic process is no change in the entropy of the subsystem, and a reversible process is define by no change of the total entropy of...
*Here, no mention of these reservoirs being a gas, so I'm not sure if I can use the PV=nRT or the P*V^(gamma)=K equation.
SO I am left with only the 1st law.
If I can write dQ1( going out from object 1)= Cp (indep of T)*(Tf-T1)
dQ2(coming into the object 2)= Cp*(T2-Tf)...
I have a compressed pure gas at a specific temperature and volume. (T1, V1) It suddenly (adiabatically) expands until it's at ambient pressure and a specific temperature. (P2, T2). Given: T1, V1, T2, and P2, I want to find P1 and V2.
There's a great example in wikipedia which is almost...
Hi,
I was doing this question and I was slightly confused as to whether I ought to just substitute n = \gamma (the adiabatic constant) into the equation? The answers don't do this, but I was wondering why it was wrong for me to do so? This was only a small fraction of the question (which was...
Using (2) on (1) give ## dU = -dW##... (4)
A.For expansion since the gas goes from ##(P_1, V_1, T_1)## to ##(P_2, V_2, T_2)##, does this imply ##T_1 \leq T_2 ##?
B. If so, then ##W## for adiabatic expansion would be negative (using (3))? Using negative ##dW## in (4) gives us a positive result...
Hi,
consider an adiabatic irreversible process carrying a thermodynamic system from initial state A to final state B: this process is accompanied by a positive change in system entropy (call it ##S_g##). Then consider a reversible process between the same initial and final system state. Such...
Homework Statement
Here's a derivation of the adiabatic PVT relationships.
QUESTION: When solving adiabatic PVT homework problems I found that I needed to express temperature in Kelvin, rather than Celsius, to get the right answers. Where in this derivation should this be specified, and how...
Homework Statement
Given a problem where air expands adiabatically with a given initial temperature, initial pressure, final pressure, and gamma (ratio of specific heats) , how would one go about solving for the final temperature? I'm just eager to get a general sense of direction.
Homework...