What is the Cv for water at different temperatures?

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SUMMARY

The discussion focuses on calculating the heat capacity at constant volume (Cv) for water as it is heated from 100°C to 500°C, particularly in the context of steam cycles. Participants highlight the challenges posed by phase changes and critical points, noting that standard steam tables often do not provide data beyond critical conditions. Key enthalpy values are provided: at 100°C and 1 atm, the enthalpy is 180.2 Btu/lb for liquid and 1150.3 Btu/lb for vapor, while at 500°C and 1 atm, it is 1499.9 Btu/lb. The discussion also touches on the limitations of efficiency in steam cycles, with a maximum coefficient of 60% established.

PREREQUISITES
  • Understanding of thermodynamic principles, particularly heat capacity and enthalpy.
  • Familiarity with steam tables, specifically ASME subcooled and superheat tables.
  • Knowledge of phase changes in water, including critical points.
  • Basic grasp of efficiency calculations in thermodynamic cycles, including Carnot efficiency.
NEXT STEPS
  • Research the properties of water at various temperatures using advanced steam tables.
  • Study the concept of heat capacity at constant volume (Cv) and its calculation methods.
  • Explore the implications of phase changes on thermodynamic efficiency in steam cycles.
  • Investigate the Carnot efficiency and its application in real-world thermodynamic systems.
USEFUL FOR

Engineers, thermodynamicists, and students studying heat transfer and steam cycle efficiency will benefit from this discussion, particularly those involved in designing and analyzing thermal systems.

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I thought about an interesting steam cycle but to calculate efficiency etc. I need to find out the Q absorbed when 1kg water is heated at constant volume from 1atm and 100C to 500C.

For this I need Cv(T), energy capacity as a function of temperature (with V constant). Maybe there is no elementary formula because of the phase change and also it will go past the critical point, so at least does anyone know any good steam tables that will have values in this range? Most of them stop a the critical point.

I can't figure out what enthlapy is for water above the critical point.
 
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Sorry about the units, I'm a Btu guy
at 100C (212F) and 1 atm (14.7 psia) enthalpy is 180.2 Btu/lb (liquid) and 1150.3 (vapor)
at 500C (932F) and 1 atm (14.7 psia) enthalpy is 1499.9 Btu/lb

from subcooled/superheat steam tables (ASME)

does that help?
 
Whatever cycle you had invented, it cannot have an efficiency coefficient higher than 60%.
 
gmax137 said:
Sorry about the units, I'm a Btu guy
at 100C (212F) and 1 atm (14.7 psia) enthalpy is 180.2 Btu/lb (liquid) and 1150.3 (vapor)
at 500C (932F) and 1 atm (14.7 psia) enthalpy is 1499.9 Btu/lb

from subcooled/superheat steam tables (ASME)

does that help?

At 500C, the pressure will not be 1 atm, it might be something like 60 atm. I'm heating this at constant volume, then expanding adiabatically back to 1 atm.

When I'm back to 1 atm, the water will be cooler (because of the work). So at this point I don't know temperature or enthlapy.

Maybe this problem is too tough to figure out.
 
Dickfore said:
Whatever cycle you had invented, it cannot have an efficiency coefficient higher than 60%.

That's what I got, too.
 
Andy Resnick said:
That's what I got, too.

Can you show how you got this? Just telling me the answer ruins the point of the exercise.
 
From my steam tables, at 101.325 kPa (0.1MPa) I have the following

at 100°C, hf=419.1, hg=2676, hfg=2256.9 (all in kJ/kg)

I assume at 100°C your steam is dry and saturated so the enthalpy is hg

at 500°C and 0.1MPa, the enthalpy is3488 kJ/kg'

As for the maximum efficiency, look up 'carnot efficiency'
 

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