# Find the value of Cp using SFEE and Thermodynamic equations

• Kajan thana
In summary, the conversation is about finding the gamma value using an equation and using it to calculate Cp for a perfect gas undergoing isentropic expansion through a turbine. The molar gas constant is equal to the universal gas constant, and Cp and Cv are related to gamma and R. The question does not mention the specific gas being used, but the gas constant and heat capacities can be expressed per unit mole or mass.
Kajan thana
Homework Statement
Find the specific heat capacity (Cp) with the given variables:

State:1.... p= 15 bars, Temperature: 600K,
State 2.... p= 1 bar, Temperature : 200, Enthalphy: -2000
This is an isentropic expansion.
Relevant Equations
Q-W=Cv(t2 -t2)
Cp/Cv= gamma
change in enthalphy = Cp * delta Temperature
I have managed to find the gamma value using the following equation: (T2/T1)= (P2/P1)(gamma-1/gamma. This will give me the answer of 1.29 SF. After this step, I am clueless.

Can someone help me with this question please?
I assume we have to find the enthalpy at state 1 to do that question.

This is not the exact statement of the problem. Please provide the exact statement.

Kajan thana
Chestermiller said:
This is not the exact statement of the problem. Please provide the exact statement.

Calculate Cp for a perfect gas that undergoes isentropic expansion through a turbine from state 1 (600K, 15bar) to state 2 where the pressure is 1 bar, the temperature is 200K and enthalpy is -2000 kJ/kg (this number is calculated from the previous question) .

Kajan thana said:
Calculate Cp for a perfect gas that undergoes isentropic expansion through a turbine from state 1 (600K, 15bar) to state 2 where the pressure is 1 bar, the temperature is 200K and enthalpy is -2000 kJ/kg (this number is calculated from the previous question) .
OK. So the -2000 is irrelevant. What did you get for gamma?

Kajan thana
Chestermiller said:
OK. So the -2000 is irrelevant. What did you get for gamma?
gamma= 1.28

Kajan thana said:
gamma= 1.28
Kajan thana said:
gamma= 1.28
Sorry the gamma is 1.68

Kajan thana said:
gamma= 1.28
OK. From that, you should immediately be able to get Cp. How are Cp and Cv related to gamma and how are they related to R?

Kajan thana
Chestermiller said:
OK. From that, you should immediately be able to get Cp. How are Cp and Cv related to gamma and how are they related to R?
The relationships are Cp - Cv = R, and Cp / Cv = Gamma. But for this question they haven't mentioned the sort of gas that is used, so we cannot find the gas constant. I'm not sure how to find the Cv or Cp. In order to find the Cv, we need the work done or the change in enthalpy. I'm not sure how to go about doing it. Thanks

Kajan thana said:
The relationships are Cp - Cv = R, and Cp / Cv = Gamma. But for this question they haven't mentioned the sort of gas that is used, so we cannot find the gas constant. I'm not sure how to find the Cv or Cp. In order to find the Cv, we need the work done or the change in enthalpy. I'm not sure how to go about doing it. Thanks
You have two equations and 2 unknowns: Cp and Cv. The molar gas constant does not depend on the gas.

Chestermiller said:
You have two equations and 2 unknowns: Cp and Cv. The molar gas constant does not depend on the gas.
Sorry I am bit confused. I thought that the molar gas constant was not the same as the universal gas constant (8.31). RGAS CONSTANT = R UNIVERSIAL CONSTANT/MOLAR MASS

Kajan thana said:
Sorry I am bit confused. I thought that the molar gas constant was not the same as the universal gas constant (8.31). RGAS CONSTANT = R UNIVERSIAL CONSTANT/MOLAR MASS
The molar gas constant is equal to the universal gas constant. The mass gas constant is equal to the universal gas constant divided by the molar mass.

Kajan thana said:
Sorry I am bit confused. I thought that the molar gas constant was not the same as the universal gas constant (8.31). RGAS CONSTANT = R UNIVERSIAL CONSTANT/MOLAR MASS
THE question doesn't have any information on the gas that is being used like the Molar Mass; apart from the mention of it being a perfect gas.

Kajan thana said:
THE question doesn't have any information on the gas that is being used like the Molar Mass; apart from the mention of it being a perfect gas.
Cp they are looking for is the molar value, not the mass value.

Chestermiller said:
Cp they are looking for is the molar value, not the mass value.
So with the simultaneous equation, I got the answer as 20 kJ/kg/K

I get 20.5

Kajan thana
Chestermiller said:
I get 20.5
yh I did the calculation wrong
Is there any other way to check the answer?

I saw this on Wikipedia, where it mentions that Rspecific = Cp -Cv. Is there something that I am misunderstanding?
Thank you.

You can express heat capacities per unit mole or per unit mass. The same goes for the gas constant. The gas constant per mole is the universal gas constant.

Kajan thana
Chestermiller said:
You can express heat capacities per unit mole or per unit mass. The same goes for the gas constant. The gas constant per mole is the universal gas constant.
Thank you

## 1. What is the significance of finding the value of Cp using SFEE and Thermodynamic equations?

The value of Cp, or specific heat at constant pressure, is an important thermodynamic property that is used to determine the amount of heat required to raise the temperature of a substance. It is also used to calculate other thermodynamic properties such as enthalpy and entropy. Therefore, finding the accurate value of Cp is crucial in understanding and predicting the behavior of a substance under different conditions.

## 2. How is the value of Cp calculated using SFEE and Thermodynamic equations?

The value of Cp can be calculated using the First Law of Thermodynamics, also known as the Steady Flow Energy Equation (SFEE). This equation takes into account the changes in energy, heat, and work of a system. It can be rearranged to solve for Cp by dividing the change in enthalpy (ΔH) by the change in temperature (ΔT). Other thermodynamic equations, such as the Ideal Gas Law and the Clausius-Clapeyron equation, can also be used to calculate Cp under specific conditions.

## 3. What factors affect the value of Cp?

The value of Cp is affected by various factors such as temperature, pressure, and the nature of the substance. In general, the value of Cp increases with an increase in temperature and decreases with a decrease in pressure. The structure and composition of the substance also play a role, as different substances have different values of Cp due to their molecular structure and intermolecular forces.

## 4. Why is it important to use SFEE and Thermodynamic equations to find the value of Cp?

Using SFEE and Thermodynamic equations to find the value of Cp allows for a more accurate and precise calculation compared to using experimental data. These equations take into account the changes in energy and work, which can be difficult to measure accurately in a real-world setting. Additionally, using these equations allows for a better understanding of the underlying principles and relationships between different thermodynamic properties.

## 5. How can the value of Cp be used in practical applications?

The value of Cp is used in various practical applications, such as in the design and optimization of thermodynamic systems, such as engines and refrigeration systems. It is also used in industries such as food processing, where the specific heat of different substances is important in determining cooking times and temperatures. In research and development, the value of Cp is used to study the thermal properties of new materials and substances.

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