Universal gas constant R= Cp-Cv

Thread starter Sabra_a
Start date Nov 7, 2019
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SUMMARY

The discussion centers on the universal gas constant R, specifically the relationship R = Cp - Cv. Participants debated whether to use delta (Δ) or differential (d) notation in their equations, concluding that the choice does not significantly impact the outcome. Additionally, there was uncertainty regarding the necessity of substituting specific values for R, K, Cv, and Cp, with a consensus that leaving the values as they are is acceptable.

PREREQUISITES

Understanding of thermodynamic principles, specifically the concepts of heat capacity (Cp and Cv).
Familiarity with the universal gas constant (R) and its applications in thermodynamics.
Knowledge of differential and delta notation in mathematical expressions.
Basic grasp of the ideal gas law and its implications in physical chemistry.

NEXT STEPS

Research the derivation and applications of the universal gas constant R in thermodynamics.
Study the differences between heat capacities at constant pressure (Cp) and constant volume (Cv).
Learn about the implications of using differential (d) versus delta (Δ) notation in thermodynamic equations.
Explore practical examples of calculating R, Cp, and Cv in real-world scenarios.

USEFUL FOR

This discussion is beneficial for students and professionals in thermodynamics, physical chemistry, and engineering fields, particularly those focusing on heat transfer and gas laws.

Nov 7, 2019

Sabra_a

Homework Statement: 1) Using the first law of thermodynamics ∆Q=∆E+∆W (Q – heat added to the system, E – internal energy of the system, W – work done by the system), the equation of state for one mole of gas PV=RT (P - pressure, V – volume, R - universal gas constant, T - temperature), and the definition of the specific heat c=∆Q/∆T derive the following equation for universal gas constant: R= cp- cv (cp and cv are specific heats at constant pressure and constant volume correspondingly).

2) The specific heats ratio or adiabatic exponent is equal by definition to k= cp/cv. Derive formulas which express specific heats at constant pressure and constant volume (cp and cv) in terms of R and k only.

Relevant Equations: First law of thermodynamics
Ideal gas equation
Specific heat

In the first question should I remove the delta and put d or that doesn't make a difference and on the second question should I substitute the values of R, K, Cv and Cp or that's not required I'm not really sure how correct is my answer to the second question