What is Isothermal: Definition and 227 Discussions

In thermodynamics, an isothermal process is a type of thermodynamic process in which the temperature of the system remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir, and the change in the system will occur slowly enough to allow the system to continue to adjust to the temperature of the reservoir through heat exchange (see quasi-equilibrium). In contrast, an adiabatic process is where a system exchanges no heat with its surroundings (Q = 0).
Simply, we can say that in isothermal process

T
=

constant

{\displaystyle T={\text{constant}}}

Δ
T
=
0

{\displaystyle \Delta T=0}

d
T
=
0

{\displaystyle dT=0}

For ideal gases only, internal energy

Δ
U
=
0

{\displaystyle \Delta U=0}

Q
=
0.

{\displaystyle Q=0.}

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1. B Change in entropy of reversible isothermal process

So I had to find change in entropy of system in reversible isothermal process. $$T\Delta S_{sys.}=Q\implies \Delta S_{sys.}=nRln\left(\frac{V_2}{V_1}\right)$$ This was good because for isothermal process ##\Delta U=0\implies Q=W## Then I read this Throughout an entire reversible process, the...
2. Irreversible isothermal Process Work External pressure not provided

It is clear that the process is isothermal else it is not possible to find heat absorbed. $$W=-P_{ext}(\Delta V)$$ However ##P_{ext}## is not given. How do I proceed? I tried taking ##W=-(P_2V_2-P_1V_1+P_3V_3-P_2V_2)=\Delta(PV)## but it is wrong for obvious reasons.
3. Reduce the pressure in an air reservoir

TRANSITIONAL REGIME: ##\dot{V}=90\, \textrm{L}/\textrm{min}=0,0015\, \textrm{m}^3/\textrm{s}## $$\dfrac{d}{dt}\int_{VC}\rho\, dV=\dot{m}\rightarrow \dfrac{d}{dt}\rho V=\dot{m}\rightarrow$$ $$\boxed{\rho_{\textrm{air}}}\rightarrow pV=R'T\rightarrow \rho =\dfrac{p}{R'T}\rightarrow 287$$...
4. Isothermal and adiabatic air compression -- different expressions

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...
5. Solving Slurry Bed Adsorption: Calculating Residence Time & Isotherm Selection

Summary:: I have an assignment on slurry bed adsorption and would like to know how to calculate residence time as it is not specified. I was also wondering if anyone had any suggestions for another isotherm to try and fit the data to (other than freundlich). Thanks ##\frac {dq} {dt} = \frac...
6. Going from 1st state to 2nd through irreversible isothermal expansion

My teacher was teaching me that how work done in isothermal reversible expansion is greater than irreversible expansion and also work done in isothermal irreversible compression is greater than that for reversible compression. He then said if someone tries to go from 1st state to the 2nd step (...
7. Reversible processes need to be ONLY isothermal or adiabatic?

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...
8. A substance has an isothermal compressibility kappa = (aT^3)/(P^2)...

Starting from v(P,T), dv=(dv/dp)_T dp + (dv/dT)_P dt i implemented conditions when T and P are constant and ended up with ln V = aT^3/P + constant and ln V = bT^3 /3P + constant If i assume that the constant is 0, i can say that a/b = 1/3 but how do i justify this assumption?
9. Gas in a syringe being compressed - thermodynamic processes

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...
10. Isothermal pressure change in a U-shaped tube

Hi, just reviewing some thermodynamics from the textbook by Sears and Salinger, having a hard time conceptualizing this one. It's an isothermal change in pressure, so the volumes of the mercury and the air both change to reach equilibrium, but if it's a "good vacuum pump", then won't the right...
11. Isothermal process involving changes in Volume and Pressure

P1 = 2 bar V1 = 5.1L P2= 1bar V2 = V1P1/P2 = 10,2L, so the volume of gas would double? or should the absolute pressure be taken into account P1= 2bar (3bar absolute), V1=5.1L P2= 1 bar V2 = 15,3L?

(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...
13. Isothermal process, Calculate the density

I can get the P2 from P1V1=P2V2 --> P2 = 10Bar, but then how do i get the density? p=p/R*T ? where p=10Bar R=287J K-1kg and T 288K, density would be 12,1kg/m3? Is that right?
14. Chemistry Calculate the Enthropy Change of Isothermal Expansion of a Non-Ideal Gas

Part (a) ΔS = ∫ (dq/T) because: dq = PdV = (nRT/V)dV Then: ΔS = ∫ (1/T)*(nRT/V)dV ΔS = nR ∫(1/V) dV ΔS =nR[ln(V2/V1)] Part (b) This is where I'm stuck. I know [P + a/(v/n)2][v/n - b] = RT can be solved for P and simplified to P = [RT/(v-b)]-[a/v2] since n=1mol But I don't know how to proceed...
15. Isothermal expansion of a gas: heat of surroundings

In an isothermal process, for an expanding gas ##\Delta U_{sys}=0## and ##Q=-W## but then, How can we evaluate ##Q_{surr} ##? It should be ##Q_{surr}=-Q_{sys}##, but I don't know how to show it in equations. If I try to get the result through the principles: ##\Delta U_{sys}=-\Delta U...
16. Can the isothermal expansion of an ideal gas be irreversible?

For the reversible expansion of an ideal gas the heat flowing out of the surroundings and into the system is equal to the work done by the system. Since both system and surroundings have the same constant temperature the entropy increase of the system is equal to the entropy decrease of the...
17. Entropy generation during irreversible isothermal expansion

Sometimes I go back and think about this stuff, and I always find something I don't understand very well. Consider an irreversible isothermal expansion of an ideal gas from state ##A## to state ##B## and suppose I know the amount of heat given to the system to perform the expansion - I'll...
18. Isothermal Processes: Ideal Gas Equation and Doubts Explained

I have become almost sure but have only some small doubts. Are all isothermal process actually ideal gas equation PV=mRT? If all such processes are occur in closed systems, this is so. Because it is isothermal the temperature is constant, R is constant and so is mass for a closed system. So the...
19. Work done in adiabatic process vs work done in isothermal

Homework Statement [/B] An ideal gas is compressed to the same volume from the same initial state for both an adiabatic and an isothermal process. In which case will more work be done ? 2. Homework Equations ##dU=dQ - dW ## ##W=\int P\,dV ##(For isothermal) ##W=nc_vdT##...
20. Isothermal Expansion w/ Equal Pressures

In an isothermal expansion of an ideal gas, can the piston be made to expand isothermally if the initial system pressure is equal to the initial surrounding pressure?(In most of the books and video lectures whenever they explain isothermal expansion, they assume initial system pressure to be...
21. Why pressure decreases during isothermal expansion?

Initially, the pressure of the gas inside the cylinder is higher than the atmospheric pressure and the piston is held in the contracted position by some means.When the piston is released, it expands and the pressure and temperature of the system decreases but the volume increases.In order to...
22. Work done for isothermal process in terms of Helmholtz func

The Helmholtz function differential form for a reversible process is: dF = -SdT - PdV, as for a reversible process δW (by system/here an (ideal) gas) = PdV and dS = δQ/T. Therefore, for a reversible isothermal process, dT = 0 and hence dF = -PdV. Therefore, the work done by the system is W =...
23. Isothermal Expansion: Explained

I am a little confused by the following; When an isothermal expansion takes place there is negative work done on the gas by the pressure, this I understand. Now by the first law the change in internal energy is equal to the heat transferred to the gas plus the work done it. So now in my script...
24. Change in entropy per mole for an isothermal process

Homework Statement Homework EquationsThe Attempt at a Solution ## dS = \frac { dQ_{rev} } { T } ## Assuming that isothermal process is a reversible processes, ## dU = dQ – pdV## For isothermal process, dU = 0. ## dQ = pdV ## ## pV = nRT##, where n is number of moles. For one mole, ##...
25. Logic applied to making isothermal assumption

Homework Statement A thin electrical heater is inserted between a long circular rod and a concentric tube with inner and outer radii of 20 and 40 mm. The rod (A) has a thermal conductivity of kA = 0.15 W/(m*K), while the tube (B) has a thermal conductivity of kB = 1.5 W/(m*K) and its outer...
26. Thermodynamics, isothermal irreversible

Homework Statement Can you please show how to solve this question (I am not asking it for homework. I am asking because it would help me understand better). Determine the entropy change in sys, surr, uni, when a sample of helium has of mass M grams at 298K and 1 bar doubles its volume in...
27. Z

Reversible Isothermal Expansion Steam

Homework Statement 2kgs (total mass) of steam goes through a revesible isothermal expansion at 500 degrees celcius. During the expansion the pressure drops from 300 kpa to 200 kpa. What is the heat absorbed by the steam during this process? Homework Equations U=W and W=nrt ln(v2/v1) The...
28. How to Calculate Work of Isothermal Magnetization?

Homework Statement A magnetic salt obeys the Curie Law μoM/Bo = C/T Where M is the magnetization, Bo is the applied magnetic field in the absence of the specimen, C is a constant, and μo is the permeability of free space. The salt is magnetized isothermally from a magnetization M1 to M2. You...
29. What is the Effect of Isothermal Movement on Internal Energy of a Gas?

Homework Statement The dot in Fig. 19-18b represents the initial state of a gas, and the isotherm through the dot divides the p-V diagram into regions 1 and 2. For the following processes, determine whether the change Eint in the internal energy of the gas is positive, negative, or zero: (a)...
30. Arrhenius Equation and pseudo isotherms

Hey, I'm doing an experiment where I run a reaction at three different microwave powers to determine if there is any effect beyond the standard temperature ramp rates. If I know how long it takes the reaction to go from 260 C to 280 C in each of these cases, is there any possible way to extract...
31. Isothermal Process: Temperature Consistency and Heat Exchange

"An isothermal process is a change of a system, in which the temperature remains constant: ΔT = 0. This typically occurs when a system is in contact with an outside thermal reservoir (heat bath), and the change will occur slowly enough to allow the system to continually adjust to the temperature...
32. A How to Solve Isothermal Incompressible Navier-Stokes for Compressible Fluid?

I did a lot of googling but could not find a satisfying answer to my question, hence a post here. Question: How to solve (or close) the isothermal incompressible Navier-Stokes equations for an isothermal compressible fluid? Situation: We have a compressible fluid, for example a gas. The flow...
33. Angular Frequency of a Piston with Ideal Gas

Homework Statement A frictionless piston of mass m is a precise fit in the vertical cylindrical neck of a large container of volume V. The container is filled with an ideal gas and there is a vacuum above the piston. The cross-sectional area of the neck is A. Assuming that the pressure and...
34. Thermodynamic Process: Is Work Conserved?

What is wrong with this logic, if any? It does not seem like this should be true but maybe I'm mistaken. Assuming the process consists of two isobaric processes and two isothermal processes the work from B to C in terms of p1, p2, V1, and V2 is given by the following. 1) WBC=p2(VC-VB) 2)...
35. Is enthelpy change during isothermal process zero?

is enthalpy change during isothermal process zero? if it is zero then what is the significance of enthalpies like enthalpy of vapourization or fussion since during phase transformation temperature remains constant.
36. Isobaric vs. isothermal expansion

We have a piston with ideal gas in it and a weight. The weight is placed on the piston. The gas is heated externally and the gas expands. Will the expansion be isobaric or isothermal? One argument would be: the expansion will be isobaric because the weight is providing constant pressure. The...
37. Thermo: isothermal, reversible expansion of ideal gas

Homework Statement Two moles of a monatomic ideal gas are at a temperature of 300K. The gas expands reversibly and isothermally to twice its original volume. Calculate the work done by the gas, the heat supplied and the change in internal energy. So: T = 300K; ΔT = 0 n = 2; R = 8.314 J K-1...
38. Isothermal Expansion of Supersonic Flow

Hi, In a standard converging-diverging rocket nozzle, we have (ex.) the relation:(1-M^2)\frac{dV}{V}=-\frac{dA}{A}By substituting in definitions, we can obtain\left(1-\frac{V^2}{\gamma R T}\right)\frac{dV}{V} = -\frac{dA}{A}This shows the dependence on temperature. The relation assumes that...
39. Would a non radiative atmosphere be isothermal?

Many credited physicists have entertained the notion of a non radiative atmosphere being isothermal as a function of height. But is this a physical reality? Many physicists accept the macroscopic conclusions of kinetic theory, the gas laws. Statistical mechanics. Experimentally verifiable...
40. Solve Isothermal Expansion: Find v2 Given P1, P2 & v1

Homework Statement Let P2 = 10^6 N/m^2, P1 = 4X10^5 N/m^2 and v = 2.5m^3/kmole Find the specific volume v2. Homework Equations Isothermal process, ideal gas. There is also a picture but it's just a generic P = constant/V plot. The Attempt at a Solution The volume given is the specific...
41. 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...
42. Isothermal (almost) compression of gas by water injection

http://www.fluidmechanics.co.uk/ I have found this by searching net. The inventor claimed that by using a new kind of piston fitted with fins, he achieved almost isothermal compression and greatly reduced the power consumption process. I want to know how much theoretically sound it is.
43. Difference between Isothermal and Adiabatic?

So for Isothermal, there is no change of T so hence delta U is 0. However, if there isn't a change of temperature, how is there a change of Q? I thought heat was the flow of energy of different temperatures. This confuses me for adiabatic as well. With no heat, how is there a temperature change...
44. Isothermal Compression of a Ideal Gas and Distance

Homework Statement The figure at the bottom shows a cylindrical tank of diameter D with a moveable 3.00-kg circular disk sitting on top. The disk seals in the gas inside but is able to move without friction. The gas inside is at temperature T. The height of the disk is initially at h = 4.00 m...
45. Entropy Change - Irreversible Isothermal Compression

Given a sample of nitrogen gas (assume ideal gas conditions), the following conditions were observed inside the container. n = 0.75 moles at 253 K, and pressure = 0.5 atm. Then, an ISOTHERMAL IRREVERSIBLE COMPRESSION on the system forced by a constant Pexternal = 10 atm reduced the initial...
46. Change in Enthelpy for Nitrogen at constant temp

Homework Statement Calculate ΔH for 2 mols of Nitrogen for the following transformation: 1 bar, 21°C → 200 bar, 21°C Given that molar Cp = 4R 2. The attempt at a solution How am I supposed to find the ΔH? From what I learned, there can only be a change in enthalpy when there's a change in...
47. I Boltzmann distribution: isothermal atmosphere error?

There is a well-known analysis of the distribution of particles by height in an isothermal atmosphere. It states that the probability of finding a particle at height ##h## is ##p(h) \propto e^{-\beta mgh}##, and then goes on to state that the number of particles at height ##h## is ##n(h) \propto...
48. Calculating Internal Energy Change: Path 2 of Carnot Cycle Question

Homework Statement A gas is to be expanded from initial stage i to final stage f along either path 1 or path 2 on a p-V diagram. Path 1 consists of three steps: an isothermal expansion(work is 23J in magnitude), an adiabatic expansion(work is 35J in magnitude), and another isothermal expansion...
49. Why boiling occurs at fix temperature?

Can anyone explain to me why does temperature of water remains constant while boiling in an open vessel or in general sense why phase transition is isothermal in nature?please give me answers from thermodynamic point of view also.
50. Entropy change in a reversible isothermal process

Why does ∆S = 0 for a reversible process, but for a reversible isothermal process, ∆S is given by nRln(Vf/Vi) (or other variations of that equation)?