Isothermal Definition and 227 Threads

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}
while in adiabatic processes:




Q
=
0.


{\displaystyle Q=0.}

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  1. C

    Isothermal expansion: reversible vs irreversible

    1. A sample of methane of mass 4.5 g occupies 12.7 L at 310 K. Assume that the gas behaves ideally. (a) Calculate the work done when the gas expands isothermally against a constant external pressure of 30.0 kPa until its volume has increased by 3.3 L. (b) Calculate the work that would be done...
  2. M

    Thermodynamics- Isothermal Expansion

    Homework Statement The temperature of 2 moles of an ideal gas is 366 K. How much work does the gas do in expanding isothermally to 2 times its initial volume? ______ J Homework Equations I think they are relevant... W= nRT ln(Vf/Vi) PV=nRT Q constant pressure= 3/2 nRT(Tf-Ti) + nR(Tf-Ti)...
  3. R

    How to calculate the heat added during an isothermal process

    Homework Statement The titleHomework Equations ?The Attempt at a Solution The only ways I know of to calculate heat are dQ = Cp.dT and dQ = Cv.dT for isochoric and isobaric process how would you go about doing it for an isothermal process Also if a system isn't a cycle but it ends up in the...
  4. M

    Question about isothermal work why heat is not affected

    What I think I understand so far: Internal energy is the sum of work done on a system and heat supplied to the system. In an isothermal case there is no change in temperature therefor internal energy has no change. therefor -q=w Question: Why is there heat? I thought heat is the energy...
  5. R

    Change in Entropy for Isothermal Expansion

    Homework Statement Derive change in entropy for Van der Waal gas in isothermal expansion TdS = ∫(dP/dV)dV + ∫(Cv/T)dT Homework EquationsP = NRT/(V-bN) + a(N/V)^2 The Attempt at a Solution TdS = ∫dP + 0 = Pf - Pi TΔS = ∫dP = ∫(Pf - Pi) TΔS = [ ∫ (NRT / Vf-bN) - a(N/Vf)^2] - [ ∫ (NRT /...
  6. C

    State Function Conditions in Isothermal, adiabatic

    In an Isothermic and reversible condition why is DH=0? (D=delta) I can understand that DU=0 but DH? but why would DH not change? DH should also =0 if it was an adiabtic and irreversible condition? since DH=dq/T -> as long as there is no heat transfer DH=0? Since it's reversible would...
  7. C

    Irreversible and isothermal work

    I know work for reversible + isothermal is w=nRTln(v2/v1) but what about irrev? I see the equation W=P(delta V) used all the time. Is this the correct one to use? or is there another equn for irreversible work for a gas? THanks
  8. G

    How to draw the Isothermal Section of a Ternary Phase Diagram

    Professor is now teaching us to draw isothermal sections of a Ternary Phase Diagram... Isothermal Section: A “horizontal” section of a ternary phase diagram obtained by cutting through the space diagram at a specified temperature I am so confused... I have big trouble in picturing the...
  9. E

    Thermodynamics - work in adiabatic, isothermal, isobaric

    Homework Statement 21. A quantity of an ideal gas is compressed to half its initial volume. The process may be adiabatic, isothermal, or isobaric. Rank those three processes in order of the work required of an external agent, least to greatest. A. adiabatic, isothermal, isobaric B...
  10. P

    Entropy change for isothermal expansion of a perfect gas

    Homework Statement At a constant temperature, 0.85 mol of an ideal gas changes its pressure from 350 Torr to 125 Torr. Calculate the entropy change for this expansion process. Homework Equations Ideal gas: PV=nRT ΔS = nRln(Vf/Vi) The Attempt at a Solution I'm stuck on how to...
  11. M

    How can I calculate final pressures in a reversible argon expansion?

    isothermal and adiabatic please help! Homework Statement Hello, I have been stuck on this problem for about an hour so any hep would be greatly appreciated! One mole of argon at 25 degrees C and 1 atm pressure is allowed to expand reversibly t a volume of 50 L (a) isothermally (b)...
  12. A

    Isothermal Expansion, No Calculus

    Homework Statement "We have some gas in a container at high pressure. The volume of the container is 444 cm^3. The pressure of the gas is 2.52e5 Pa. We allow the gas to expand at constant temperature until its pressure equals atmospheric pressure, which is 0.857e5 Pa." A. Find the work...
  13. K

    Thermodynamics, Isothermal Question

    Homework Statement 10 moles of an ideal gas, in the initial state P1 = 10 atm, T1 = 300K are taken around the following cycle. a) A reversible change of state along a straight line path on the P-V diagram to the state P = 1 atm T = 300K. How much work is done during the cycle...
  14. H

    Isothermal expansion/compression

    Maybe somebody can explain this to me and I will have a better understand of the Isothermal expansion problem. Here is what I know: \DeltaU(T)=0 but internal energy is also a state function. So if I expand from P1,V1 to P2,V2 isothermally then how can internal energy not change. Internal...
  15. E

    Rate of change of pressure with volume, adiabatic vs isothermal conditions

    Homework Statement For a particular sample of monatomic gas, the rate of change of pressure with volume under isothermal conditions is -2 x 10^7 Pa m^-3. Calculate the rate of change under adiabatic conditions. Homework Equations isothermal: dP/dV = -2 x 10^7 Q = nRTln(Vf/Vi)...
  16. G

    Isothermal Process: Constant Temperature & Internal Energy

    I understand that an isothermal process occurs at constant Temperature. And for an ideal gas, the the internal energy is a function of temperature only. Therefore, when Temp = 0, then U = 0 also, meaning the internal energy of the gas doesn't change... and we have q = - w or basically q = PΔV...
  17. J

    [Thermo.] thermal expansion and isothermal compressibility coefficients.

    Homework Statement A certain metal whose thermal expansion coefficient \beta is 5,0 × 10^-5 °C^-1 and whose isothermal compressibility \kappa_T is 1,2 × 10^-6 atm^-1 is at an initial pressure of 1 atm and an initial temperature of 20°C. A thick layer of Invar is thermally insulating the...
  18. R

    Gas Cycle Process; Adiabatic, Isovolumetric and Isothermal

    Homework Statement A monatomic gas has V1 P1 and T1 (volume pressure and temp) at state 1 The gas then goes through the following process adiabatic expansion to stage 2 (exapands to twice its volume) isovolumetric heating so it gets back to T1; stage 3 isothermal compression back to...
  19. K

    Isothermal reversible condensation

    Homework Statement A sample of 1.00 mol H20(g) is condensed isothermally and reversibly to liquid water at 100°C. The standard enthalpy of vaporization of water at 100°C is 40.656 kJ mol-1. Find w, q, change in internal energy, and change in enthalpy for this process. Homework Equations...
  20. P

    Calculating Work, Volume, and Energy Change for Isothermal Compression

    Homework Statement A 2.00-mol sample of helium gas initially at 300K and 0.400 atm is compressed isothermally to 1.20atm. Assume the helium behaves as an ideal gas, find (a) the final volume of the gas, (b) the work done on the gas, and (c) the energy temperature?Homework Equations PV = nRT W...
  21. E

    Enthelpy and isothermal, where is my logic wrong

    Assume ideal gas and isothermal : \Delta H = \int_{T_{i}}^{T_{f}}\! C_{p} dT = 0 (no change in temperature, no change in enthalpy) \Delta H = \Delta U + W, U = 0 There is no change in internal energy but there is change in work done. How do these two contradicting statements work.
  22. J

    Finding the work done by a gas under quasi-static, isothermal expansion

    1. So, an ideal gas is initially at 293K and 200kPa, and has a volume of .004m3 It undergoes a quasi-static, isotheral expansion until its pressure is reduced to 100kPa What is the Work done by the gas 2.I know that for isothermal conditions W=nRTln(Pf/Pi) 3. my first attempt was...
  23. P

    Can adiabatic process be isothermal?

    As the title says. If we have a system which can't exchange heat with the environment that is, by definition, an adiabatic process. Is it possible that in that situation the pressure lowers, the volume increases and the temperature stays the same?
  24. S

    Is an adiabatic process isothermal also?

    Is an adiabatic process isothermal also? Can anyone please tell me if it is necessary for an adiabatic process to be isothermal? Please explain with example.
  25. J

    First law of thermodynamics, q=w for a reversible isothermal process

    according to first law of thermodynamics,q=w for a reversible isothermal process.this means all the energy absorbed is being used to to do the work ,but according to second law of thermodynamics,there cannot be 100% effeciency.please tell where i am going wrong
  26. I

    Is there any process adiabatic and isothermal?

    Homework Statement Is it possible to have a process that is both adiabatic and isothermal. Homework Equations The Attempt at a Solution I think the answer is no. Because when a system is doing an adiabatic process, the total energy of this system must be changed. For an...
  27. S

    Enthelpy change of an isothermal process

    what is the enthalpy change of an isothermal process?(Why is it 0?)
  28. M

    Solving Isothermal Expansion Problem - Temperature Calculation

    Homework Statement Suppose 161 moles of a monatomic ideal gas undergoes an isothermal expansion as shown in the figure (attached). The horizontal axis is marked in increments on 20 m3 What is the temperature at the beginning and at the end of this process? Homework Equations PV = nRT...
  29. A

    How to Model an Isothermal Core in a Simplified Star?

    Homework Statement Let’s make an idealized star model with two parts: an isothermal helium core, and pure hydrogen layers outside the core. The core represents the part where hydrogen has already been burned. Mathematically this represents the simplest model that might resemble a...
  30. I

    Calculating Isothermal Expansion Heat, Work, Internal Energy and Entropy

    i was given this test problem a couple of days ago, that ha2 parts: 1 mol of ideal a) isothermal reversible at a Ti, Pi = 3 atm, Pf= 1 atm b)irreversible isothermal expansion under constant pressure (1 atm) . find the heat/work/internal energy, delta(H), entropy for both. attempt: part a...
  31. M

    How to Calculate Final Volume and Pressure in Isothermal Process"

    Hey all, If i have an isothermal process of an ideal monotomic gas, IE. deltaT = 0 and i have an initial volume (V1) and an initial pressure (P1). Then I am given the work done BY the gas (W = -### as it is the environment providing the energy) How do i calculate the final volume and the...
  32. D

    Thermo Question on isothermal expansion

    Homework Statement I have a mixture of saturared water liquid vapor mixture at 200 c, volume = .03 m^3 at 15.54 Bars... the mixture undergoes an isothermal expansion and the volume doubles, what is the new pressure? mtotal = .301 kg Homework Equations this is my prob not sure which...
  33. E

    Derive the expression for isothermal change in Constant Volume Heat Capacity

    Homework Statement Derive the following expression for calculating the isothermal change in Constant Volume Heat Capacity: (dCv/dV)T = T(d2P/dT2)V Homework Equations The Attempt at a Solution I have no idea, please help
  34. Z

    Calculating isothermal copressibility and expansion coefficient

    Homework Statement Calculate the isothermal compressibility and the expansion coefficient of a van der waals gas. Then show using Euler's chain relation that KR = alpha(Vm-b) Homework Equations isothermal compressibility K = (-1/V) (dv/dp)t isothermal expansion alpha= (1/v)(dv/dt)p...
  35. W

    How to Calculate Work in Isothermal Reversible Expansion Using Virial Equation?

    Homework Statement Calculate the work done during the isothermal reversible expansion of a gas that satisfies the virial equation of state. Homework Equations Virial equation of state: pVm = RT(1+B/Vm + C/Vm + ...) Isothermal reversible expansion: w = -nRT ln(Vf/Vi) The Attempt at a...
  36. A

    Isothermal Process Homework: Calculate Q(in) & Q(out)

    Homework Statement Calculate Q(in) and Q(out). Homework Equations Specific Heat: Cv = 5/2 R R = 8.314 J/mol K The Attempt at a Solution For the process C-> A, it is an isothermic process but we are not given temperature. The equation to finding the total work done from C->A is nRT...
  37. 1

    Understanding the Isothermal Process: Temperature and Internal Energy Explained

    Urgent!Isothermal process Hi guys. i have a very short question. In an isothermal process, change is temperature is zero, so change in internal energy is zero, thus Q=W. The part that i am confused is that if Q=mc(deltaT) then should be a change in temperature in the isothermal process? Thanks...
  38. I

    Why Does Work Equal ∫ p dv in an Isothermal Process?

    i was told that w= p dv but how come w= pv dv in a isothermal process??
  39. J

    Isothermal Expansion: Heat Transfer in a Confined Ideal Gas

    Homework Statement During an isothermal expansion, a confined ideal gas does -150J agaisnt its surroundings. Which of the following describes the heat transfer during this process? A 150J of Heat was added to the gas B 150J of Heat was removed from the gas C 300J of Heat was added to the...
  40. M

    Isothermal Expansion: Work and Heat

    Which of the following statements are true? 1. Heat is converted completely into work during isothermal expansion. 2. Isothermal expansion is reversible under ideal conditions. 3. During the process of isothermal expansion, the gas does more work than during the isobaric expansion...
  41. K

    Solving the Isothermal Constant Volume A = B + C Reaction

    Homework Statement Reaction: A = B + C Reaction is run in an isothermal constant volume reaction vessel. Initially, before any reaction has occurred, the vessel is filled with pure A at 1 atm and 400K. The equilibrium conversion, epsilon and final pressure of the system is to be...
  42. K

    Isothermal Expansion - Work and Heat

    Homework Statement I have most of these figured out (it is 4 and 5 that are causing me problems) but I figured that I may as well post the answers that I have already gotten because they may be relevant. The answers that I got are in bold. 1. Which of the curves in the figure represents an...
  43. J

    Isothermal expansion and final pressure

    Homework Statement a monatomic ideal gas(Cv=3/2R) undergoes an isothermal expansion at 300K, as the volume increased from 0.09m^3 to 0.36m^3. the final pressure is 100kPa. the change in the internal energy of the gas, in kJ is closest to a. 0 b. 25 c. -50 d. -25 e. 50 Homework...
  44. D

    Isobaric, Isochoric, Isothermal, and Adiabatic Processes

    http://session.masteringphysics.com/problemAsset/1013990/12/1013990E.jpg Which of the following statements are true about the first half of this process, just going from state A to state F? Both T and U increase. W provides energy input. Q provides energy input. Q is larger (in...
  45. L

    Thermodynamic Application Isothermal Work

    Homework Statement One mole of an ideal gas does 3000 J work on its surroundings as it expands isothermally to a final pressure of 1 atm and volume 25 L. Determine a) initial volume and b) Temp of gas Homework Equations The Attempt at a Solution Well, its isothermal, so Temp is...
  46. C

    Equation for work of a reversible isothermal compression

    I need to find the equation for the work of a reversible isothermal compression of 1 mol of a gas in a piston/cylinder assembly if the molar volume of the gas is given by V= ((RT)/P) + b where b and R are positive constants. Not sure what to do .. please help! THANKS
  47. C

    Please help with this thermo problem Its an isothermal expansion.

    Homework Statement 10 moles of an ideal gas at 100 atm pressure are expanded isothermally against a constant pressure of 10 atm, to 10 at. calculate Q W deltaU and delta H (Take temp to be T)Homework Equations PV = nRT DeltaH = Q (for constant P) DeltaU = Q-W U = H+PV W = Integral(PdV)The...
  48. A

    Trying to work out isothermal heat transfer

    Homework Statement A gas mass 0.115kg undergoes an increase in volume from 0.25m cubed to 0.56m cubed. initial temp 32 degrees c and initial pressure 1.2bar. work out heat transfer?? Homework Equations W=P1V1 ln(V2/V1) W=mRT ln(V2/V1) P1V1/T1=P2V2/T2 Q=U2-U1+W PV=mRT The Attempt...
  49. S

    Computing work in an isothermal process

    I was reviewing some notes on the Carnot cycle and noticed that to compute the work done along an isotherm you take the integral of PdV from the initial to final volume. What value do you use for P since P is not held constant on an isothermal curve? Why is P treated as a constant?
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