Finding a relationship using 1st Law of Thermodynamics

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SUMMARY

The discussion focuses on deriving a relationship involving dq/T, dT/T, dp/p, Cp, and R for an ideal gas using the First Law of Thermodynamics. The key equations utilized include dq = dU + dW, du = Cv*dT, and the ideal gas equation p(alpha) = RT. The user successfully derived dq = Cp*dT - R*T*dp/p and suggested dividing both sides by T to achieve the desired relationship. This approach confirms the validity of the derivation and provides a clear path to the solution.

PREREQUISITES
  • Understanding of the First Law of Thermodynamics
  • Familiarity with ideal gas laws and equations
  • Knowledge of specific heat capacities (Cp and Cv)
  • Basic calculus for manipulating equations
NEXT STEPS
  • Study the derivation of the First Law of Thermodynamics in detail
  • Learn about the relationship between Cp, Cv, and R for ideal gases
  • Explore applications of the ideal gas equation in thermodynamic processes
  • Investigate the implications of specific heat in real-world scenarios
USEFUL FOR

Students studying thermodynamics, engineers working with ideal gases, and anyone interested in the principles of energy conservation in physical systems.

Charanjit
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1. Homework Statement

Derive a relationship between dq/T , dT/T, dp/p , Cp , and R for an ideal gas.

2. Homework Equations

dQ = dU + dW and/or dq = du + dw (for a unit mass)
p*d(alpha) = dw (alpha = specific volume V/m)
du = Cv*dT
p(alpha) = RT (Ideal gas equation, a different form)
Cv + R = Cp


3. The Attempt at a Solution

I went through the derivation and got the following:

dq = Cp*dT - R*T*dp/p

I have no clue what to do from here. Any help? Or is this correct?
 
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After posting this, I found something, why not divide both sides by T, that will give us the relationship the question wanted right?
 

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