The specific heat ratio using molar analysis.

Question

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Answer 1

Question

Chapter 12.9, Problem 1E

To determine

The specific heat ratio using molar analysis.

Expert Solution & Answer

Answer to Problem 1E

The specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

Explanation of Solution

Write the expression to calculate the specific heat ratio of mixture km contains H2,O2 and CO using the following relation from molar analysis.

km=(cp)m(cv)m (I)

Here, the specific heat at constant pressure of the mixture is (cp)m, the specific heat at constant volume of the mixture is (cv)m.

Write the expression for specific heat at constant pressure of the mixture (cp)m.

(cp)m=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,CO (II)

Here, the mass fraction of hydrogen is mfH2, the mass fraction of oxygen is mfO2, the mass fraction of carbon monoxide is mfCO, the specific heat capacity at constant pressure of hydrogen at 300 K is cp,H2, the specific heat capacity at constant pressure of oxygen at 300 K is cp,O2, and the specific heat capacity at constant pressure of carbon monoxide at 300 K is cp,CO.

Write the expression for specific heat at constant volume of the mixture (cv)m.

(cv)m=mfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO (III)

Here, the specific heat capacity at constant volume of hydrogen at 300 K is cv,H2,the specific heat capacity at constant volume of oxygen at 300 K is cv,O2, specific heat capacity at constant volume of carbon monoxide at 300 K is cv,CO.

Conclusion:

Substitute Equation (II) and (III) in (I).

km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO

Thus, the specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

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Answer 2

Question

Chapter 12.9, Problem 1E

To determine

The specific heat ratio using molar analysis.

Expert Solution & Answer

Answer to Problem 1E

The specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

Explanation of Solution

Write the expression to calculate the specific heat ratio of mixture km contains H2,O2 and CO using the following relation from molar analysis.

km=(cp)m(cv)m (I)

Here, the specific heat at constant pressure of the mixture is (cp)m, the specific heat at constant volume of the mixture is (cv)m.

Write the expression for specific heat at constant pressure of the mixture (cp)m.

(cp)m=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,CO (II)

Here, the mass fraction of hydrogen is mfH2, the mass fraction of oxygen is mfO2, the mass fraction of carbon monoxide is mfCO, the specific heat capacity at constant pressure of hydrogen at 300 K is cp,H2, the specific heat capacity at constant pressure of oxygen at 300 K is cp,O2, and the specific heat capacity at constant pressure of carbon monoxide at 300 K is cp,CO.

Write the expression for specific heat at constant volume of the mixture (cv)m.

(cv)m=mfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO (III)

Here, the specific heat capacity at constant volume of hydrogen at 300 K is cv,H2,the specific heat capacity at constant volume of oxygen at 300 K is cv,O2, specific heat capacity at constant volume of carbon monoxide at 300 K is cv,CO.

Conclusion:

Substitute Equation (II) and (III) in (I).

km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO

Thus, the specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

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Answer 3

Question

Chapter 12.9, Problem 1E

To determine

The specific heat ratio using molar analysis.

Expert Solution & Answer

Answer to Problem 1E

The specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

Explanation of Solution

Write the expression to calculate the specific heat ratio of mixture km contains H2,O2 and CO using the following relation from molar analysis.

km=(cp)m(cv)m (I)

Here, the specific heat at constant pressure of the mixture is (cp)m, the specific heat at constant volume of the mixture is (cv)m.

Write the expression for specific heat at constant pressure of the mixture (cp)m.

(cp)m=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,CO (II)

Here, the mass fraction of hydrogen is mfH2, the mass fraction of oxygen is mfO2, the mass fraction of carbon monoxide is mfCO, the specific heat capacity at constant pressure of hydrogen at 300 K is cp,H2, the specific heat capacity at constant pressure of oxygen at 300 K is cp,O2, and the specific heat capacity at constant pressure of carbon monoxide at 300 K is cp,CO.

Write the expression for specific heat at constant volume of the mixture (cv)m.

(cv)m=mfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO (III)

Here, the specific heat capacity at constant volume of hydrogen at 300 K is cv,H2,the specific heat capacity at constant volume of oxygen at 300 K is cv,O2, specific heat capacity at constant volume of carbon monoxide at 300 K is cv,CO.

Conclusion:

Substitute Equation (II) and (III) in (I).

km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO

Thus, the specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

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Answer 4

Question

Chapter 12.9, Problem 1E

To determine

The specific heat ratio using molar analysis.

Expert Solution & Answer

Answer to Problem 1E

The specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

Explanation of Solution

Write the expression to calculate the specific heat ratio of mixture km contains H2,O2 and CO using the following relation from molar analysis.

km=(cp)m(cv)m (I)

Here, the specific heat at constant pressure of the mixture is (cp)m, the specific heat at constant volume of the mixture is (cv)m.

Write the expression for specific heat at constant pressure of the mixture (cp)m.

(cp)m=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,CO (II)

Here, the mass fraction of hydrogen is mfH2, the mass fraction of oxygen is mfO2, the mass fraction of carbon monoxide is mfCO, the specific heat capacity at constant pressure of hydrogen at 300 K is cp,H2, the specific heat capacity at constant pressure of oxygen at 300 K is cp,O2, and the specific heat capacity at constant pressure of carbon monoxide at 300 K is cp,CO.

Write the expression for specific heat at constant volume of the mixture (cv)m.

(cv)m=mfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO (III)

Here, the specific heat capacity at constant volume of hydrogen at 300 K is cv,H2,the specific heat capacity at constant volume of oxygen at 300 K is cv,O2, specific heat capacity at constant volume of carbon monoxide at 300 K is cv,CO.

Conclusion:

Substitute Equation (II) and (III) in (I).

km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO

Thus, the specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

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Answer 5

Chapter 12.9, Problem 1E

To determine

The specific heat ratio using molar analysis.

Expert Solution & Answer

Answer to Problem 1E

The specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

Explanation of Solution

Write the expression to calculate the specific heat ratio of mixture km contains H2,O2 and CO using the following relation from molar analysis.

km=(cp)m(cv)m (I)

Here, the specific heat at constant pressure of the mixture is (cp)m, the specific heat at constant volume of the mixture is (cv)m.

Write the expression for specific heat at constant pressure of the mixture (cp)m.

(cp)m=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,CO (II)

Here, the mass fraction of hydrogen is mfH2, the mass fraction of oxygen is mfO2, the mass fraction of carbon monoxide is mfCO, the specific heat capacity at constant pressure of hydrogen at 300 K is cp,H2, the specific heat capacity at constant pressure of oxygen at 300 K is cp,O2, and the specific heat capacity at constant pressure of carbon monoxide at 300 K is cp,CO.

Write the expression for specific heat at constant volume of the mixture (cv)m.

(cv)m=mfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO (III)

Here, the specific heat capacity at constant volume of hydrogen at 300 K is cv,H2,the specific heat capacity at constant volume of oxygen at 300 K is cv,O2, specific heat capacity at constant volume of carbon monoxide at 300 K is cv,CO.

Conclusion:

Substitute Equation (II) and (III) in (I).

km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO

Thus, the specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

Answer 6

Chapter 12.9, Problem 1E

To determine

The specific heat ratio using molar analysis.

Expert Solution & Answer

Answer to Problem 1E

The specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

Explanation of Solution

Write the expression to calculate the specific heat ratio of mixture km contains H2,O2 and CO using the following relation from molar analysis.

km=(cp)m(cv)m (I)

Here, the specific heat at constant pressure of the mixture is (cp)m, the specific heat at constant volume of the mixture is (cv)m.

Write the expression for specific heat at constant pressure of the mixture (cp)m.

(cp)m=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,CO (II)

Here, the mass fraction of hydrogen is mfH2, the mass fraction of oxygen is mfO2, the mass fraction of carbon monoxide is mfCO, the specific heat capacity at constant pressure of hydrogen at 300 K is cp,H2, the specific heat capacity at constant pressure of oxygen at 300 K is cp,O2, and the specific heat capacity at constant pressure of carbon monoxide at 300 K is cp,CO.

Write the expression for specific heat at constant volume of the mixture (cv)m.

(cv)m=mfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO (III)

Here, the specific heat capacity at constant volume of hydrogen at 300 K is cv,H2,the specific heat capacity at constant volume of oxygen at 300 K is cv,O2, specific heat capacity at constant volume of carbon monoxide at 300 K is cv,CO.

Conclusion:

Substitute Equation (II) and (III) in (I).

km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO

Thus, the specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

Answer 7

Chapter 12.9, Problem 1E

To determine

The specific heat ratio using molar analysis.

Answer 8

Expert Solution & Answer

Answer to Problem 1E

The specific heat ratio using molar analysis is km=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,COmfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO.

Answer 9

Expert Solution & Answer

Answer 10

Expert Solution & Answer

Answer 11

Explanation of Solution

Write the expression to calculate the specific heat ratio of mixture km contains H2,O2 and CO using the following relation from molar analysis.

km=(cp)m(cv)m (I)

Here, the specific heat at constant pressure of the mixture is (cp)m, the specific heat at constant volume of the mixture is (cv)m.

Write the expression for specific heat at constant pressure of the mixture (cp)m.

(cp)m=mfH2⋅cp,H2+mfO2⋅cp,O2+mfCO⋅cp,CO (II)

Here, the mass fraction of hydrogen is mfH2, the mass fraction of oxygen is mfO2, the mass fraction of carbon monoxide is mfCO, the specific heat capacity at constant pressure of hydrogen at 300 K is cp,H2, the specific heat capacity at constant pressure of oxygen at 300 K is cp,O2, and the specific heat capacity at constant pressure of carbon monoxide at 300 K is cp,CO.

Write the expression for specific heat at constant volume of the mixture (cv)m.

(cv)m=mfH2⋅cv,H2+mfO2⋅cv,O2+mfCO⋅cv,CO (III)

Here, the specific heat capacity at constant volume of hydrogen at 300 K is cv,H2,the specific heat capacity at constant volume of oxygen at 300 K is cv,O2, specific heat capacity at constant volume of carbon monoxide at 300 K is cv,CO.