Can anyone help thermodynamics specific heat

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SUMMARY

The discussion focuses on deriving the ratio of specific heats, CP/CV, using TDS equations. The user has attempted to equate TDS equations 1 and 3 but encounters difficulties in simplifying the resulting equation. The relevant equations mentioned are TDS 1: CVDT + T(DP/DT)vDV = TDS 1, TDS 2: CPDT - T(DV/DT)pDP = TDS 2, and TDS 3: CV(DT/DP)vDP + CP(DT/DV)pDV = TDS 3. The user seeks clarification on the correct application of these equations and assistance with the mathematical manipulations required to derive the specific heat ratio.

PREREQUISITES
  • Understanding of thermodynamics principles, specifically the concepts of specific heat.
  • Familiarity with TDS (Temperature, Density, and Entropy) equations in thermodynamics.
  • Basic calculus and differential equations for manipulating thermodynamic equations.
  • Knowledge of the relationship between pressure, volume, and temperature in thermodynamic systems.
NEXT STEPS
  • Study the derivation of the specific heat ratio CP/CV using TDS equations.
  • Learn about the implications of TDS equations in thermodynamic processes.
  • Practice solving thermodynamic equations involving partial derivatives.
  • Explore advanced topics in thermodynamics, such as Maxwell's relations and their applications.
USEFUL FOR

Students and professionals in thermodynamics, particularly those studying or working in fields related to heat transfer, energy systems, and physical chemistry.

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Explaining your reasoning, show that the ratio of the specifc heat is

CP/CV = (DP/DV)s / (DP/DV)t

hint :use TDS EQUATIONS

I have used tds equation 3 and tds equation 1 and equated them,but i am stuck because i get to an equation like


(CP/CV-1)(DT/DV)p = T(DP/DT)v and just do not know how to get to the ratio

how i used the wrong equations or is it my maths skills,please help:bugeye:
 
Physics news on Phys.org
We don't know what these equations are. What are TDS equations 1 and 3.
 
CVDT + T(DP/DT)vDV = TDS 1

CPDT - T(DV/DT)pDP = TDS 2


CV(DT/DP)vDP + CP(DT/DV)pDV = TDS 3
 

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