What is Adiabatic expansion: Definition + 96 Threads
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.
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
$$\delta q=0\tag{1}$$
$$\delta w=-P_2dV\tag{2}$$
$$dU=C_VdT\tag{3}$$
$$dU=-P_2dV\tag{4}$$...
Does the work "extracted" from a gas (with the same initial properties) against a piston while expanding change based on the mass of the piston?
For example, I have a specific volume of compressed air inside a cylinder with a piston positioned horizontally with stops. The air temperature is...
Task:
A thermally insulated pressurized air cylinder, B, was initially placed inside a closed-bottom, circular hollow cylinder A with an inner diameter of 50 cm. Then a tightly fitting, frictionless sliding piston with a mass of 20 kg was installed. Using the outlet valve, the height of the...
I was checking bait cannons and potato guns on the internet because they are fun. Maybe one day I'll build my own.
First of all, these cannons use multiple sources of energy (combustion using hair spray, dry ice, etc.). I'll just consider compressed air cannons because I think they are the most...
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...
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 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...
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...
I've seen the derivation for the adiabatic expansion of an ideal gas which gives the result ## TV^{\gamma - 1} = constant ## which I understand. I have also seen the a similar result, ## pV^{\gamma} = constant ##. But I can't see how to get from the first expression to the second. Any ideas?
I am trying to figure out how you can subcool a dewar of liquid oxygen (vacuum insulated) just by releasing the pressure sitting on top of it. The liquid I am thinking of in this case is liquid oxygen, which boils at -297.33 F at 1 atm. Let's say I fill a dewar with LO2, then pressurize that...
Homework Statement
Adiabatic expansion of an ideal gas is carried out in a steady flow process. The initial pressure of the gas is 2.5 bar. The volume is expanded from 1.2m3 to 3.8m3. Heat capacity ratio (γ) = 1.42. Calculate enthalpy change of the process.
Homework Equations
PV = nRT
W = ∫...
Homework Statement
I do not know if I am allowed to have two question in one post, so forgive me if I am breaking a rule. These two are frustrating me as I cannot see where the error in my process is.
1) A 1.00-mol sample of an ideal diatomic gas, originally at 1.00 atm and 10 ∘C, expands...
Homework Statement
A sample of 1.60 mol H2 (Cv = 20.5 J K-1 mol-1) at 21°C and 1.50 atm undergoes a reversible adiabatic compression until the final pressure is 4.50 atm. Calculate the final volume of the gas sample and the work associated with this process. Assume that the gas behaves ideally...
This seems simple, but I have some confusion. I'm trying to refine a numerical simulation to get away from my isothermal assumption, to account instead for isentropic temperature and pressure changes in pressure tank with an orifice.
Given an insulating air tank of volume ##V##, containing air...
As in the title, I'm trying to establish the approximate velocity (sans friction and other losses) of a pellet propelled by compressed gas from a tank. Below is what I have came up with myself, I would appreciate if someone could review this as say whether the end values are reasonable.
I have...
As a follow-on to this thread, which in turn followed this closed thread, I'm starting a new thread on a related real-world problem.
Say I have a 2-liter plastic soda bottle filled partway with water, and pressurized. It has been sitting inverted (with the opening pointed down, and sealed) for...
Homework Statement
I'm stuck on part (c) of this question.
Homework Equations
$$T\frac{d}{dT}\bigg(\frac{L}{T}\bigg) \equiv \frac{dL}{dT} - \frac{L}{T}.$$
Clausius-Clapeyron equation:
$$ \frac{dp}{dT} = \frac{L}{T\Delta V} \approx \frac{L}{TV_{vap}}.$$
The Attempt at a Solution
My approach...
Homework Statement
Calculate the change in internal energy of an ideal gas the expands reverisbly and adiabatically from ##v_i## to ##v_f##
Homework Equations
##pV^{\gamma} = constant ##*, where ##\gamma=\frac{c_p}{c_v}##
for a reversible adiabatic.
##E=\alpha p V##, ##\alpha## a constant...
Homework Statement
An ideal monatomic gas has initial pressure Po and occupies initial volume Vo. The gas undergoes an adiabatic expansion in which the volume is doubled. Calculate in terms of Po and Vo
a) the final pressure of the gas
b) the change in its enthalpy during the...
I want to know if a specific amount of gas has been compressed isothermaly an then released to expand freely, how much of the energy that has been spent on compressing the gas can be recovered. As for example, 1 gm-mole of Nitrogen has been compressed to 1/4th of its initial volume from at 1...
Homework Statement
Suppose that an infinite square well has width L , 0<x<L. Nowthe right wall expands slowly to 2L. Calculate the geometric phase and the dynamic phase for the wave function at the end of this adiabatic expansion of the well. Note: the expansion of the well does not occur at...
I am studying for a thermo exam, and one of the problems I am doing deals with adiabatic expansion of a piston in a cylinder. When solving for work, the solution guide uses m*Cv*(T2-T1). I don't understand why they know how to use Cv instead of Cp. The pressure changes, so obviously you wouldn't...
Homework Statement
The problem is in the context of convection in the troposphere
Show that when an ideal gas expands adiabatically, the temperature and pressure are related by the differential equation
\frac{dT}{dP} = \frac{2}{f+2} \frac{T}{P}
Homework Equations
Ideal gas law PV = nRT...
I've read in my texts that the there are two kinds of Molar Specific Heat Capacities for gases:
1. Molar Specific Heat Capacity at constant Volume ----- ##C_v##
2. Molar Specific Heat Capacity at constant Pressure ---- ##C_p##
And in case of Constant temperature there is no point in...
Homework Statement
A gas consisting of diatomic molecules that can rotate but not oscillate at a given range of temperatures expands adiabatically from pressure of 365Pa and volume of 70m3, doing 101J of work, while expanding to a final volume. What is its final PV (pressure volume) product...
Homework Statement
A saturated water vapor mix in a 0.05m3 piston-cylinder at 200C with a quality of 0.5 expands adiabatically, producing 500kJ work with a final temperature of 50C. Find:
a) final quality
b) change in entropy[/B]
Homework Equations
Q-W=ΔU
x=(vavg-vf)/(vg-vf)
uavg=uf+xufg...
Hello guys, I have some troubles to understand a reversible adiabatic expansion.
we have dq=0 and dw=-pdV and for a perfect gas dU= Cv*dT. I don't really understand why dU= Cv*dT since we have a variation of volume and it is established that dU= Cv*dT when we haven't any modification of the...
Homework Statement
The energy and pressure of black body radiation depend on T and V as Eq(1) & Eq(2). Suppose that the temperature and volume of a box of radiation change adiabatically. Find the relation between dE and dT in this process. Next, using Eq(1), show that T ∝V^-1/3
Homework...
I have some homework that I am just not able to figure out.
There is a 2kg parcel of air at T1=32°C and p1= 0.8 atm
This parcel of air expands until it is at T2=12°C
Also, during the expansion 3.2 g of water will condense due to the dT (ΔvapH (water) = 40.65kJ mol-1
Also: Cv=0.718 kJ...
Homework Statement
In an adiabatic irreversible expansion of ideal gas , if Pext = 0 then which is true,
A. T2=T1
B. Q=0,
C. P1V1= P2V2
D. P1V1γ= P2V2γ
Homework Equations
ΔU = Q - W
For ideal gas, PV= nRT[/B]
ΔU ∝ ΔT
The Attempt at a Solution
I know Q= 0,
Work done is zero,
So ΔU = 0, hence...
Homework Statement
Which of the following changes during the free adiabatic expansion of a real gas?
(I) internal energy
(II) temperature
(III) pressure
Homework Equations
PV=nRT; ΔU= q + w
The Attempt at a Solution
For ideal gases under adiabatic conditions, we know that there is no heat...
This example is taken from the wikipedia page describing irreversible processes.
I just want to make sure I understand correctly why the initial state can't be reached anymore. I assume the transitions to be quasi-static, but there is friction between the piston and the cylinder. If so...
Homework Statement
I am trying to derive the formula for time varying thrust given that I know the initial mass/volume of water in a water rocket. Knowns will include initial pressure, initial volume of water, and nozzle cross sectional area.
Homework Equations
Bernoullis equation: (p/ρg) +...
Homework Statement
Prove the relationship between the pressure, P, and the temperature, T, for an ideal gas with a reversible adiabatic expansion. Base the proof on the first law of thermodynamics and the ideal gas law.
The relationship is: T^(Cp,m/R)/P = constant
Where R is the gas constant...
My textbook says, basically, for an adiabatic process...
All three variables in the ideal gas law—P, V, and T—change during an adiabatic process.
Let’s imagine an adiabatic gas process involving an infinitesimal change in volume dV and an accompanying infinitesimal change in temperature dT. The...
I am having trouble calculating the work done by a product gas in reversible adiabatic expansion, and in calculating the final temperature. pV gamma = constant, Cv = constant (assume), gamma = cv + nR / Cv.
anyone who can help me out?
Homework Statement
a) For a certain ideal gas CP = 8.58 cal mol-1 K-1. We have 2 moles of said gas at 293.15 K and 15 atm. Calculate the final volume and temperature when the gas expands adiabatically and reversibly until it reaches a pressure of 5 atm. (Answers: V = 7.45 L; T = 227.15 K)
b)...
Homework Statement
Part(a): Show dL/dT can be expressed as:
Part(b): Show L = L0 + ΔCT for an indeal gas
Part(c): Show the following condition holds for an adiabatic expansion, when some liquid condenses out.
Homework Equations
The Attempt at a Solution
Finished parts (a)...
Homework Statement
1 mole of an ideal gas initially at 100° C and 10 atm is expanded adiabatically against a constant pressure of 5 atm until equilibrium is re-established. Given that the temperature dependence of the heat capacity is CV = 18.83 + 0.0209T calculate deltaU, deltaH and deltaS...
Homework Statement
Show that \frac{dp}{p} =\frac{\gamma}{\gamma-1}\frac{dT}{T} if the decrease in pressure is due to an adiabatic expansion.Homework Equations
Poisson equations:
Pv^{\gamma}
Tv^{\gamma - 1}
Ideal Gas Law:
Pv=R_{d}T, where R_{d} is the dry air gas constant.
Hydrostatic...
I'm new to the forum, so please be kind.
I was reading through my pchem textbook, and I noticed something. We're given the equation:
ΔU = q + w
For an adiabatic expansion, we're told that q = 0. Fair enough, no heat transfer. But when there is a constant T and change in V, my book...
Homework Statement
1 mol of monoatomic ideal gas (temperature T1) is inside a cylinder with a moving piston (all are isolated). The initial external pressure on the piston is P1. at some point the external pressure is changed to (2/3)P1, the gas undergoes (irreversible) adiabatic expansion...
what is the change In internal energy of an ideal gas when it is expanded Adiabatically from (p °,v°) to ( p,v )?
The relevant equations :
dQ= dU+ pdv ; pV^ r = K (constant). r = Cp / Cv.
Attempted solution :
During adiabatic process dQ=0 ; p= k v ^ -r
Th f r : du= -k v^ -rdv
Integrating...
Homework Statement
Consider the adiabatic expansion of .553mol of an ideal monatomic gas with CV,m = 3R/2. The initial state is described by P = 6.25bar and T = 306K. Calculate the final temperature if the same gas undergoes an adiabatic expansion against an external pressure of P = 1.25bar to...
Homework Statement
A 3.25 mol sample of an ideal diatomic gas expands adiabatically from a volume of 0.1050 m^3 to 0.762 m^3. Initially the pressure was 1.00 atm
Determine the initial and final temperatures
Homework Equations
PVγ= nRT
The Attempt at a Solution
To get the initial...
Homework Statement
We start with an ideal gas confined to half a container. Then, without heat flow, the gas flows into the other half as the partition is punctured. Find the new temperature after the expansion.
Homework Equations
Since there is no heat flow, I assume the process is...
Question:
in a bicycle pump the preasure increases from [p1 = 10^5] to [p2 = 30^5]. If the process is adiabatic ant the air starts at [T1 = 293 K], find the maximum temperature of the air in the pump. (Assuming air can be treated as an ideal gas)
Attempt:
So using the 1st Law and given...