Isothermal Definition and 216 Threads

∫Homework Statement Compress a body reversibly and isothermally from P1 to P2. How much heat goes in or out?Homework Equations Maxwells four relations, differential forms of the four thermodynamic potentials (Central, Enthalpy, Gibbs, Helmholtz) The Attempt at a Solution My problem is that...

Homework Statement Derive an expression for the amount of work done when one mole of an ideal gas expands isothermally at a temperature T from an initial volume V1 to a final volume V2. Homework Equations PV = nRT W = V2∫V1Pdv The Attempt at a Solution I'm not really sure how to go...

Homework Statement A system containing 10kg of water undergoes a reversible isothermal process. The initial state can be characterized as saturated vapor at 300°C. The pressure in the final state is 1MPa. The heat transfer during the process in (inKJ) Homework Equations Q = m(U2-U1)+W...

β is expansibility , (1/V)(∂V/∂T) at constant temperature κ is isothermal compressibility , (-1/V)(∂V/∂P) at constant pressure How to prove (∂P/∂T) at constant V = (β/κ) Thank you

Homework Statement Two identical samples of ideal gas are initially at P1 and V1. The first sample undergoes an isothermal transformation to P2, V2 and second sample undergoes an adiabatic transformation to P3, V2. If P3<P2, is V2 higher or lower than V1? Explain Homework Equations...

Can we define specific heat capacity for an adiabatic process ?? Would it always be zero since dQ is 0 for an adiabatic process? Also, can we define specific heat capacity for isothermal processes ? Would it be infinity in all cases? Just want to verify if I am thinking along the...

Here's the textbook way of calculating the work done by an ideal gas in an isothermal case. PV=nRT P.dV=(nRT/V).dV ∴ ∫P.dV=nRT∫dV/V → W2-W1=nRT*ln(V2/V1) My question. Consider a cylindrical (or of any other shape) container of surface area A and a frictionless movable piston attached...

Hey all, I was wondering if someone could explain the difference between isothermal and adiabatic processes. I know that in isothermal process, there is no temperature change in the system, and in adiabatic process, there is no heat transfer. However, can someone explain to me what each one is...

Homework Statement For an ideal gas, undergoing a quasistatic process, the equations below are correct. Evaluate them given that we have an isothermal process Homework Equations PV^\alpha=K where K is a constant and \alpha=C-C_P/C-C_V W = \frac{K}{\alpha -1}...

Homework Statement I have a general concept inquiry. I was doing some thermal homework, and calculating values of Q in a given cycle. One process was isothermal, however it turned out that Q was not zero, causing me to wonder: How can there be a heat transfer in an isothermal process...

Heat is defined as "the transfer of energy owing to a temperature difference between two bodies". Consider a gas expanding against a massless frictionless piston. Assume that the process is both isothermal and reversible, and that the gas is ideal, so that its internal energy does not change...

http://www.pichem.net/images//reversible-adiabatic//adiabatic-expansion-2.jpg Evidently the adiabatic curve is steeper than the isothermal curve. How can I prove this mathematically using the following facts: P_{1}V_{1} = P_{2}V_{2} for a reversible isothermal process...

Homework Statement I have hydrogen in a 12 L tank, at T=15 C. Some of it is used, the T = const. and Δp=0.4 MPa, the molar mass of hydrogen is M=2*10^-3 J/(mol*K). Find the mass of the used hydrogen. Homework Equations Am I wrong in simply using: \Delta m=\frac{M}{RT}V\Delta p ...

Homework Statement Variables: N (number of particles), μ (chemical potential), P (pression), V (volume). k is Boltzmann's constant. I often use β=1/kT. The (isothermal) compressibility is given by \kappa_{T} = -\frac{1}{V}\left (\frac{\partial V}{\partial P}\right )_{N,T} The...

Homework Statement In the graph attached, why is isothermal graph line higher than adiabatic one?? Homework Equations The Attempt at a Solution At first, i had thought that work done in an isothermal process is greater than in an adiabatic process...but for comparison we would...

Homework Statement In calculus, the work done when a gas expands from volume V1 to volume V2 is given by W = ∫V2V1 P dV Use this expression to show that the work done by n moles of gas at temperature T during an isothermal expansion from volume V1 to V2 is W = nRT ln(V2/V1) Homework...

Homework Statement An ideal gas of N particles is reversibly expanded from V1 to V2 = 4V1. The starting temperature T1 is known and E_1 = \frac{3}{2} N k_B T_1. As of yet E_2 is unknown. a) Express \Delta E = E_1 - E_2 in terms of the added heat Q and work done on the gas W. b) Calculate...

Homework Statement A projectile of mass M kg is accelerated from rest to V m/s using a compressed air cannon. conceptually, we may consider the projectile to be a frictionless "piston" within a cylinder that is closed at one end and open to the atmosphere at the other end. Before firing...

Homework Statement A 740g quantity of an ideal gas undergoes a reversible isothermal compression at a temperature of 330 K. The compression reduces the volume of the gas from 0.40 m3 initially, to 0.32 m3 finally. The entropy change of the gas is equal to: A) -43 J/K B) -150 J/K...

Homework Statement Homework Equations Work done by an ideal gas, isothermal process: W=n*R*T*ln(V_f / V_i) Work, constant-pressure process: W=p*(V_f - V_i) The Attempt at a Solution I first tried plugging n=1, R=8.31, T=273.15, V_f=17.5 L, V_i=24 L into the first equation and it...

Homework Statement A thermally isolated chamber is pumped down to a very low pressure. At some point, the chamber is vented slowly so that it is filled with air up to atmospheric pressure, whereupon the valve is closed. The temperature of the air surrounding the chamber is T0=300 K. What is...

i'm entirely confused with this. with analyzing each definition: adiabatic process : a thermodynamic process in which there is no transfer of heat if a system is in state (P1, V1, T1) → (P2, V2, T2) if it is adiabatic no heat transfer occurs, if no heat transfer occurs the two states must be...

Homework Statement A compressor is required to drive acetylene gas at 1.85 kg/s through a horizontal pipe, 68.7 m long. The maximum pressure that may be developed by the compressor is to be found, and gas pressure at the delivery end of the pipeline must be 470 kPa. The system is to...

For a process at constant pressure, ΔH=q. My textbook clearly says that the only way that enthalpy can change is with a change in temperature. So ΔH=0. But q≠0 for an isothermal process. I know that ΔU=0 for an isothermal process. So ΔH=0+Δ(PV)=Δ(nRT)=0 It really seems like ΔH should...

Homework Statement Is work greater in adiabatic or isothermal process? A piston with oxygen has a final volume 1/4 the initial. The temperature is also 5 times greater. Determine pressure change, heat released or absorbed, and work done on or by gas. Homework Equations the work for adiabatic...

Homework Statement In a reversible isothermal expansion of an ideal gas, as the gas expands, heat is supplied to it, so that the temperature remains constant. Thus, temperature and hence kinetic energy of the molecules does not change but the 'disorder' of the gas increases as it occupies a...

I have these two homework problems, as well as solutions. What I do not understand is why the solution for one is not the solution for the other. First problem: A sample consisting of 1.00 mol Ar is expanded isothermally at 0 deg Celc from 22.4 dm3 to 44.8 dm3 reversibly. Calculate q, w, delta...

Homework Statement To a very good approximation, ammonia obeys the Bertholet equation of state, which readsPV=nRT+\frac{9}{128}(\frac{nRTc}{Pc})(1-6\frac{Tc^2}{T^2})Pa)Suppose we have 500 grams of ammonia under a pressure of P=3.04 atm and at T=323K. Calculate the volume of ammonia according...

If U, H are functions of T only, then ΔU and ΔH should be zero for isothermal processes ΔG and ΔA are only defined at constant T (thus define isothermal processes) ΔG = ΔH – TΔS thus equals -TΔS always (since ΔH=0)? this makes no sense since from previous calculations I have done in many...

1. Homework Statement Two equal masses of an ideal gas initially at the same temperature and pressure are compressed to half of their initial volumes, one of them isothermally, and the other while thermally isolated from its surroundings. Which one of the following is the same for both...

Hi, Adiabatic, iosbaric and isochoric processes are good approximations for a lot of thermodynamic phenomena in every day life. But the conditions for a process to be isothermal are so artificial that i have grave difficulties to fudge a story. Are there any examples of thermal...

1 mole of an ideal gas is compressed isothermally from 1 to 10 bar at 298 K. Calculate the total entropy change associated with this process if it is carried out 1) Reversibly 2) Irreversibly S (system) =nRln(vf/vi) for an isothermal process. I think I am getting a bit...

Homework Statement 200W of power is required for an isothermal process of a larger cyclic process. Use the first law of thermodynamics to calculate the amount of heat power that is generated by the isothermal process. Homework Equations Change in heat energy = change in internal energy +...

1.>Consider a gas in a vessel with a piston on top.Let it expand to a greater volume. So, delta H=delta U+delta(PV) but delta U is 0 as it is isothermal. now,as the number of moles of gas remains constant,delta(PV) is nR(delta T) which is again 0. SO delta H is 0. Thats what my book says...

Isothermal problem! Imagine an idead cylinder and piston and gas filled in it with the Pgas=Patm. Ideal gas Equation for initial state is PV=nRT for the gas....(1) Now is dQ heat is imparted to the gas. Pressure of the gas at that instant increases by dP so it expands by dV to attain...

I have a question on the quantity -(dV/dP)T,N where V = volume, P = pressure, T = temp, N = number of moles and T, N are held constant. I see in textbooks that this quantity is always positive at equilibrium. It makes intuitive sense, as if it were negative, it would be unphysical. I've been...

On any smooth surface one can choose isothermal coordinates in a neighborhood of any point. What is the physical interpretation of this fact? Do the isothermals describe an equilibrium distribution of temperature? How would that be true say on a sphere?

Homework Statement Air with the mass of 10kg, with pressure 15 bar and temperature 50 C comes to a isobaric expansion to 3 times the original volume, then the air cools to the pressure of 6 bar(isovolumetricly). After that it comes to adiabatic expansion to original temperature (50 C i guess)...

Homework Statement I have a diagram of a process of a monoatomic gas. and the problem is that I know that the total amount of work = total amount of heat, so there is no internal energy change. why? because my process started at the same temp that it finished. how ever... it is asking me...

What are Internally reversible processes and why isothermal processes are reversible? Also, Isothermal process are only internally reversible or they can be "externally" reversible?

I am reviewing material for my thermodynamics class and one of the practice exams says that the change in enthalpy during an isothermal process is equal to zero. This doesn't make any sense to be considering.. \Delta H = \Delta U + PV and since this is an isothermal process.. \Delta U =...

Homework Statement Calculate the increase in internal energy of 1 kg of water at 100 degrees Celsius when it is converted into steam at the same temperature and at 1atm. The density of water and steam are 1000kg/m3 and 0.6kg/m3 resp. The latent heat of vaporisation of water is 2.25 x 106...

Homework Statement One mole of monatomic ideal gas is taken from an initial pressure(P) and volume(V) to a final pressure(2P) and volume(2V). It goes from pressure=P and volume=V to pressure=P/2 and volume=2V through isothermal expansion and from there volume stays constant but the pressure...

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...

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)...

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...

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...

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 /...

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...

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