4 replies to this topic

[James-Zhou]

the thermodynamic parameters of saturated steam at 2000Kpa is：
P1=2000Kpa,
t1=212.2℃,
intencity 10.0338kg/m³,
enthalpy H1=2799.7 kj/kg

and the parameters at 20000Kpa is :
P2=20000Kpa,
t2=365.6℃,
intencity 176.5961kg/m³,
enthalpy H2=2364.2 kj/kg

then according to H =U+PV
H1-H2=(U1-U2)+(P1V1-P2V2)
=>U1-U2=(H1-H2)-(P1V1-P2V2)>0
=>U1>U2
means : with the temperature dropping ,the internal energy is increasing ! its not sensible !
Do someone know how can this happen ?

[kkala]

1. Comparison to other steam tables shows insignificant differences, except for H2=2418.2 kJ/kg. Using your figures, P1V1-P2V2=2000/10.0338 - 20000/176.5961 kPa*m3/kg=86.07 kJ/kg (of steam). H1-H2=435.5 kJ/kg, so U1-U2=349.4 kJ/kg
2. For ideal gases, U depends only on temperature and increases with it.
For real gases, like van der Waals gases, U also increases with (specific) volume increase. In above change from state 2 to state 1, this volume increase seems to predominate over temperature decrease, resulting in increase of internal energy U.
3. See M W Zemansky, "Heat and Thermodynamics", Energy Equation, Internal energy of a van der Waals gas.
4. Seeing that it is hard to "feel" increase of U with decrease in temperature, let us assume that steam goes isothermally (365.7 oC) from state 2 to 2000 kPa, then isobarically to state 1 (212.4 oC). Using Water97-v13.xla add-in for convenience, internal energy U goes from about 2300 to 2900, then to 2600 kJ/kg. More exact values in attached "steamU.xls". This indicates predominant influence of (specific) volume increase for the specific conditions, despite the decrease in temperature.
Note: For mentioned add-in, see http://www.cheresour...water-and-steam '> http://www.cheresour...water-and-steam . This software can be downloaded free from Web.

[kkala]

SteamU.xls reported in previous post No 2 is attached here.
For downloading mentioned add-in, see http://www.cheresour...ater-and-steam/ '> http://www.cheresour...ater-and-steam/ .

Attached Files

•  steamU.xls   29.5KB   452 downloads

Edited by kkala, 11 November 2012 - 04:19 PM.

[narendrasony]

Old topic but still relevent.

As Kkala has pointed out, for real gases internal energy is not the function of temperature alone. Here is another explanation:

 

Internal energy is sum of Molecular kinetic energy (Translational , rotational and vibrational) and potential energy due to molecular attraction forces.

 

For ideal gases, since there are no molecular attraction forces, potential energy term is zero and internal energy is only the sum of kinetic energies which is a function of temperature alone.

 

For real gases, molecular attraction forces become significant particularly at high pressures and it reduces overall internal energy. So, at higher pressures as you increase the pressure at given temperature, internal energy decreases.

You can go from State-1 to State-2 as Kkala mentioned in Point (4) of post-2, you may see that as the pressure is increased from 2000 KPa to 20,000 KPa at 365.7 DegC, internal energy goes down from 2900 to 2300 Kj/Kg. Potential energy becomes predominant.

 

Regards

Narendra

[kkala]

Interesting and comprehensible explanation, based on gases kinetic theory. Thanks, Narendra.