Universal gas constant R= Cp-Cv

In summary, the Universal Gas Constant R is a physical constant denoted by the symbol R that relates the energy of a system to its temperature and pressure. It has a value of approximately 8.314 J/mol*K and is also known as the molar gas constant. It is important in thermodynamics as it is used in equations to relate properties of gases, calculate changes in enthalpy and internal energy, and determine the ideal gas law constant. Its relationship to specific heat capacities Cp and Cv is given by the equation R = Cp - Cv and its units vary depending on the units used for pressure, volume, and temperature.
  • #1
Sabra_a
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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
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  • #2
Leave it alone. It looks fine.
 
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Thank you
 

1. What is the value of the universal gas constant (R)?

The universal gas constant, denoted by the symbol R, has a value of 8.314 J/mol·K. This value is used in various equations and calculations involving gases.

2. What is the significance of the universal gas constant?

The universal gas constant is a fundamental constant in physics and chemistry. It relates the physical properties of gases, such as temperature, pressure, and volume, to each other and allows for the calculation of various thermodynamic quantities.

3. How is the universal gas constant related to specific heat (Cp and Cv)?

The universal gas constant, R, is equal to the difference between the specific heat at constant pressure (Cp) and the specific heat at constant volume (Cv). This relationship is expressed as R = Cp - Cv.

4. What are the units of the universal gas constant?

The units of the universal gas constant are joules per mole per Kelvin (J/mol·K). This unit is a combination of the SI units for energy (joules), amount of substance (moles), and temperature (Kelvin).

5. How is the universal gas constant used in the ideal gas law?

The ideal gas law, PV = nRT, incorporates the universal gas constant, R, to relate the pressure (P), volume (V), amount of substance (n), and temperature (T) of an ideal gas. This law is used to predict the behavior of gases under various conditions and is a fundamental concept in thermodynamics.

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