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.

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1. ### Chemistry A few questions on an irreversible adiabatic expansion of an ideal gas

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 $$\delta q=0\tag{1}$$ $$\delta w=-P_2dV\tag{2}$$ $$dU=C_VdT\tag{3}$$ $$dU=-P_2dV\tag{4}$$...
2. ### A Work done during adiabatic expansion on piston

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...
3. ### Adiabatic Expansion of Pressurized Air in a Piston-Cylinder Setup

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...
4. ### Optimization of barrel length in pneumatic cannons

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...
5. ### I Adiabatic expansion work far exceeds isobaric of same volume, why?

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...
6. ### New volume of balloon after adiabatic expansion

Result My attempt
7. ### Adiabatic expansion with temperature-dependent gamma

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...
8. ### Adiabatic expansion of a piston in a cylinder filled with ideal gas

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...
9. ### I How Do You Calculate Initial Pressure and Final Volume in Adiabatic Expansion?

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...
10. ### I Description of Adiabatic Expansion

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?
11. ### Thermodynamics question: venting a tank of liquid oxygen

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...
12. ### Thermodynamics - Enthelpy change in adiabatic expansion

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 = ∫...
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### How Do You Solve Adiabatic Expansion Problems in Thermodynamics?

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...
14. S

### Work and Volume in Adiabatic Expansion

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...
15. ### Final pressure and temperature knowing only air mass outflow

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...
16. ### Final velocity of an air rifle pellet from compressed gas

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...
17. ### Pressure and temperature of expanding humid air

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...
18. ### Condition for condensation from adiabatic expansion

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...
19. ### I Explain Graphs -- adiabatic Expansion of mono- di- and poly- gas

"How it can be explained mathematically by dP/dV = -gammaP/V
20. ### Reversible adiabatic expansion -- calculate change in E

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...
21. ### Adiabatic expansion of an ideal gas

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...
22. ### Isothermal compression and adiabatic expansion

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...
23. ### Adiabatic expansion of infinite square well

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...
24. ### Thermodynamics, use of Cv and Cp

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...
25. ### Adiabatic Expansion Pressure Temperature Relation

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...
26. ### Molar Specific Heat (gas) at varying pressure and volume?

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...
27. ### Adiabatic Expansion of a Gas: Final Pressure-Volume Product Calculation

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...
28. ### Adiabatic expansion of a saturated vapor mix: Δx, ΔS

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...
30. ### Relationship Between V and T in Adiabatic Expansion

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...
31. ### Calculating reversible adiabatic expansion

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...
32. ### Irreversible adiabatic expansion in which P_ext=0

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...
33. ### What Changes During Free Adiabatic Expansion of a Real Gas?

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...
35. ### Variable mass calculation of thrust for a water rocket

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) +...
36. ### Reversible adiabatic expansion proof

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...
37. ### Should Adiabatic Work Include VdP?

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...
38. ### Work done by product gas in reversible adiabatic expansion

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?
39. ### Adiabatic expansion against constant pressure

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)...
40. ### Liquid-Vapour Interface: Adiabatic Expansion

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)...
41. ### Adiabatic expansion with temperature dependent heat capacity.

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...
42. ### Decrease in pressure due to adiabatic expansion derivation?

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...
43. ### Adiabatic Expansion: Constant pressure and temperature

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...
44. ### Adiabatic expansion, entropy change

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...
45. ### Change in internal energy due to adiabatic expansion of ideal gas

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...
46. ### Irreversible Adiabatic Expansion (Physical Chemistry)

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...
47. ### Determine initial and final temperatures, adiabatic expansion?

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...
48. ### Why Does Temperature Remain Constant in Adiabatic Free Expansion?

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...
49. ### Joule free adiabatic expansion dT=0?

In that experiment , the internal energy is zero , volume increase , pressure of system decrease, then temperature will constant ? Thanks
50. ### (THERMO) - Adiabatic Expansion - known P1, P2, and T1

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...