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The entropy of a mixture of ideal gases is the sum of the entropies of constituents evaluated at:
- a)Temperature and pressure of the mixture
- b)Temperature of the mixture and the partial pressure of the constituents
- c)Temperature and volume of the mixture
- d)Pressure and volume of the mixture
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The entropy of a mixture of ideal gases is the sum of the entropies of...
The entropy of a mixture of ideal gases is equal to the sum of the entropies of the component gases as they exist in the mixture. We employ the Gibbs-Dalton law that says each gas behaves as if it alone occupies the volume of the system at the mixture temperature. That is, the pressure of each component is the partial pressure.
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The entropy of a mixture of ideal gases is the sum of the entropies of...
Entropy of a mixture of ideal gases
The entropy of a mixture of ideal gases can be determined by considering the entropy of the individual constituents.
Temperature and Volume
The entropy of a mixture of ideal gases is a function of temperature and volume. This means that the entropy of each constituent can be evaluated at the temperature and volume of the mixture.
Additive property of entropy
The entropy of a mixture of ideal gases is an additive property. This means that the total entropy of the mixture is equal to the sum of the entropies of the individual constituents.
Formula
Mathematically, this can be expressed as:
S_mix = ∑(S_i(T_mix, V_mix))
Where S_mix is the entropy of the mixture, S_i is the entropy of the ith constituent, T_mix is the temperature of the mixture, and V_mix is the volume of the mixture.
Conclusion
Therefore, option C is the correct answer as the entropy of a mixture of ideal gases is the sum of the entropies of constituents evaluated at temperature and volume of the mixture.
The entropy of a mixture of ideal gases can be determined by considering the entropy of the individual constituents.
Temperature and Volume
The entropy of a mixture of ideal gases is a function of temperature and volume. This means that the entropy of each constituent can be evaluated at the temperature and volume of the mixture.
Additive property of entropy
The entropy of a mixture of ideal gases is an additive property. This means that the total entropy of the mixture is equal to the sum of the entropies of the individual constituents.
Formula
Mathematically, this can be expressed as:
S_mix = ∑(S_i(T_mix, V_mix))
Where S_mix is the entropy of the mixture, S_i is the entropy of the ith constituent, T_mix is the temperature of the mixture, and V_mix is the volume of the mixture.
Conclusion
Therefore, option C is the correct answer as the entropy of a mixture of ideal gases is the sum of the entropies of constituents evaluated at temperature and volume of the mixture.
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The entropy of a mixture of ideal gases is the sum of the entropies of...
For an ideal gas mixture, the entropy can be calculated based on the properties of the individual gases making up the mixture. The key factor here is how the entropy of each constituent gas is evaluated in the context of the mixture's overall properties.
Here's a breakdown of how entropy typically depends on state variables for an ideal gas:
- Entropy as a function of temperature and pressure: This is a common way to express the entropy, but it may not be directly additive for a mixture due to the pressure term varying for each gas due to its partial pressure.
- Entropy as a function of temperature and partial pressure: While individual gas entropies could be calculated this way, summing them does not straightforwardly account for the interactions in the mixture's volume or the total pressure.
- Entropy as a function of temperature and volume: For a mixture, if each gas were to occupy the total volume V of the mixture at the mixture's temperature T, the entropy of each gas can be calculated separately and then summed. This approach utilizes the fact that ideal gases do not interact chemically, and each gas expands or contracts to fill the entire volume independently of others. The entropy calculation then considers each gas's partial pressure implicitly through its mole fraction in the mixture and the total volume.
- Entropy as a function of pressure and volume: This would require additional information about the temperature to compute the entropy since temperature is a key variable affecting entropy changes and values.
Thus, for calculating the entropy of a mixture of ideal gases where the entropies of the constituents are additive, the most practical and typical approach uses the mixture's temperature and the total volume that the mixture occupies. Therefore, the correct answer is:
C: Temperature and volume of the mixture
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The entropy of a mixture of ideal gases is the sum of the entropies of constituents evaluated at:a)Temperature and pressure of the mixtureb)Temperature of the mixture and the partial pressure of the constituentsc)Temperature and volume of the mixtured)Pressure and volume of the mixtureCorrect answer is option 'C'. Can you explain this answer? for Mechanical Engineering 2025 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about The entropy of a mixture of ideal gases is the sum of the entropies of constituents evaluated at:a)Temperature and pressure of the mixtureb)Temperature of the mixture and the partial pressure of the constituentsc)Temperature and volume of the mixtured)Pressure and volume of the mixtureCorrect answer is option 'C'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The entropy of a mixture of ideal gases is the sum of the entropies of constituents evaluated at:a)Temperature and pressure of the mixtureb)Temperature of the mixture and the partial pressure of the constituentsc)Temperature and volume of the mixtured)Pressure and volume of the mixtureCorrect answer is option 'C'. Can you explain this answer?.
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