Isothermal reversible condensation

In summary, the change in energy is equal to the change in enthalpy, but the changes in internal energy and enthalpy are not equal because the change in temperature is zero.
  • #1
kido
6
0

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




The Attempt at a Solution



So since this is an isothermal reversible compression, change in temperature is equal to 0, so change in internal energy should also be equal to 0.
Because deltaH = deltaU + delta(pV), and for an ideal gas pV = nRT so deltaH = 0 + delta(nRT) = 0, change in enthalpy should also be equal to 0.

HOWEVER the solutions were quite different. Apparently deltaH = -standard enthalpy of vapourization, q = deltaH, w = -(external pressure) x deltaV, and deltaU = q + w.

What am I missing here? Why are the changes in internal energy and enthalpy not zero if the change in temperature is zero?

I know this is probably a really basic thermodynamics question but I just don't get it!
 
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  • #2
Liquid water is not an ideal gas.
 
  • #3
okay, so what are the expressions for deltaU and deltaH for a liquid?
 
  • #4
kido said:
okay, so what are the expressions for deltaU and deltaH for a liquid?

Exactly what is given in the answer: the change in enthalpy is the enthalpy of vaporization. Condensation releases heat, so this value is negative. And by definition, the change in energy is the enthalpy without the work performed during the process.
 
  • #5
Okay, i understand that now, thanks. There's one more thing that i am having trouble understanding, though. In the solutions, it says that because the condensation is done isothermally and reversibly, the external pressure is constant at 1atm.
I thought the whole point of a reversible process was that the pressure was not constant? Shouldn't the expression for work be
w = -nRTln(Vf/Vi),
not w = -(external pressure)*(Vf-Vi)?
 
  • #6
Reversibility doesn't imply anything about the pressure being constant or not constant. And work is always [itex]\int P(V)\,dV[/itex]. For ideal gases at constant temperature this expression can be reduced to the other expression you give, but again, we're not dealing with an isolated ideal gas here.
 
  • #7
Ah, I see. I really must learn which expressions apply only to ideal gases!
So because this question mentions the standard enthalpy of vaporization, the external pressure is at standard conditions, which is 1atm?
Thank you very much for your help.
 
  • #8
I am having the same problems in this question. Not sure if I did it correct.
I said "Delta H = -Enthalpy of Vaporization"
"W=0" because the final state (liquid) does not alter volume
"Delta H = q " this is true for isothermal processes
"Delta U= q + W, W=0 so Delta U=q"

is this thought correct?
 

FAQ: Isothermal reversible condensation

What is isothermal reversible condensation?

Isothermal reversible condensation is a process in thermodynamics where a gas is cooled to its dew point temperature and condenses into a liquid. This process occurs at a constant temperature, meaning no heat is added or removed from the system.

What is the difference between isothermal and adiabatic condensation?

The main difference between isothermal and adiabatic condensation is the presence of heat transfer. In isothermal condensation, the temperature remains constant throughout the process, while in adiabatic condensation, the temperature changes due to heat transfer.

What are the applications of isothermal reversible condensation?

Isothermal reversible condensation is used in various industries, such as chemical and pharmaceutical, to separate and purify gases. It is also used in refrigeration systems to convert gases into liquids, such as in air conditioning units.

How does isothermal reversible condensation relate to the Clausius-Clapeyron equation?

The Clausius-Clapeyron equation describes the relationship between temperature and vapor pressure for a substance undergoing a phase change, such as from a gas to a liquid. Isothermal reversible condensation follows this equation, as the temperature remains constant while the pressure and vapor pressure change during the condensation process.

What factors can affect the efficiency of isothermal reversible condensation?

The efficiency of isothermal reversible condensation can be affected by several factors, including the temperature difference between the gas and the surrounding environment, the pressure of the gas, and the surface area available for condensation. Additionally, the type of gas being condensed and its chemical properties can also impact the efficiency of the process.

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