What is the Cv for water at different temperatures?

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Discussion Overview

The discussion revolves around determining the specific heat capacity at constant volume (Cv) for water at various temperatures, particularly in the context of a steam cycle. Participants explore the challenges of calculating energy absorption when water is heated at constant volume from 100°C to 500°C, especially considering phase changes and conditions above the critical point.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant seeks Cv(T) for water and mentions the difficulty in finding an elementary formula due to phase changes and conditions above the critical point.
  • Another participant provides enthalpy values for water at 100°C and 500°C, indicating that at 500°C, the pressure will not be 1 atm and may be around 60 atm.
  • Concerns are raised about the efficiency of the proposed steam cycle, with a claim that it cannot exceed 60% efficiency.
  • Participants share links to steam tables, but one notes that the maximum temperature in a referenced database is below the desired range.
  • Enthalpy values are provided in kJ/kg for water at 100°C and 500°C, with assumptions made about the state of the steam at these temperatures.
  • Discussion includes a reference to Carnot efficiency as a theoretical limit for the cycle's efficiency.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of calculating Cv and the efficiency of the steam cycle. There is no consensus on the maximum efficiency or the conditions affecting enthalpy at higher temperatures.

Contextual Notes

Limitations include the dependence on specific steam tables, potential out-of-range errors for temperature data, and unresolved assumptions regarding the state of water and steam during the heating and expansion processes.

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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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