Specific Heat Constant Volume Question

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SUMMARY

The discussion centers on calculating the specific heat at constant volume (Cv) for air using the specific heat at constant pressure (Cp) and the ideal gas constant (R). The equation provided for Cp is: Cp = 1.9327e-10*T^4 - 7.9999e-7*T^3 + 1.1407e-3*T^2 - 4.4890e-1*T + 1.0575e+3. It is established that Cv can be derived from Cp using the formula Cv = Cp - R. The conversation also highlights the importance of using a spreadsheet for calculations and curve fitting to analyze Cv and Cp at various pressures and temperatures.

PREREQUISITES
  • Understanding of specific heat concepts (Cp and Cv)
  • Familiarity with the ideal gas law and the ideal gas constant (R)
  • Basic knowledge of thermodynamics
  • Proficiency in using spreadsheet software for data analysis
NEXT STEPS
  • Research the specific heat equations for various gases, focusing on air.
  • Learn how to perform curve fitting in spreadsheet applications like Microsoft Excel or Google Sheets.
  • Explore the use of Perry's Chemical Engineering Handbook for thermodynamic properties.
  • Investigate the impact of pressure and temperature on specific heat values for gases.
USEFUL FOR

Engineers, thermodynamics students, and anyone involved in the study of gas properties and heat transfer will benefit from this discussion.

Gordon Arnaut
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Can someone give me the equation to calculate the change of Cv (specific heat at constant volume with change in temperature.

For example the equation to do this with Cp (specific heat at constant pressure) is:

Cp = 1.9327e-10*T^4 - 7.9999e-7*T^3 + 1.1407e-3*T^2 - 4.4890e-1*T + 1.0575e+3


Regards,

Gordon.
 
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Look up the equation for the given substance in a table. For example, Perry's Chemical Engineering Handbook. What substance is the equation for cp valid for? If it's an ideal gas, you can use the ideal gas constant to get a relationship between cp and cv.
 
Sorry, forgot to mention the gas is air.

Yeah, I can get Cv once I know Cp, by subtracting R:

Cv = Cp - R.

I was just wondering if there was an equation because I want to use it in a spreadsheet.


Regards,

Gordon.
 
Gordon Arnaut said:
Sorry, forgot to mention the gas is air.

and the air isn't frozen, nor superheated to some obscene temperature, right? then, is not C_v, C_p, and R constant with repect to T? i don't follow the premise to your original question.
 
Cp= Cv + R
 
Hi Gordon,
Attached is the output from a spreadsheet that gives Cv and Cp at various pressures and temperatures. Just do a curve fit.

Edit: Pressure in PSIA
 

Attachments

Last edited:
Thanks, Q.

What is the underlying equation?

Regards,

Gordon.
 

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