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Which one of the following expression is true for Tds equal to
- a)dh - VdP
- b)dh + VdP
- c)dh - PdV
- d)dh + Pd
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which one of the following expression is true for Tds equal toa)dh - V...
Tds = du+ PdV— First Tds equation .
Tds - dh- VdP— Second Tds eauation
Tds - dh- VdP— Second Tds eauation
Most Upvoted Answer
Which one of the following expression is true for Tds equal toa)dh - V...
Understanding Tds and Thermodynamic Relationships
In thermodynamics, Tds (where T is temperature and ds is the change in entropy) is a fundamental expression that relates various state functions. To understand why option 'A' (Tds = dh - VdP) is correct, we need to explore the relationships between enthalpy (h), pressure (P), and volume (V).
Key Thermodynamic Definitions
- Enthalpy (h): Defined as h = u + Pv, where u is internal energy and Pv is the pressure-volume work.
- Entropy Change (ds): This represents the change in the disorder or randomness of a system.
Using the First Law of Thermodynamics
- The first law connects changes in internal energy (du), heat added (Q), and work done (W):
du = dQ - dW.
- For a reversible process, the heat transfer can be expressed as Tds.
Derivation of Tds = dh - VdP
1. Starting Point: Begin with the first law in differential form.
2. Enthalpy Differential: The differential of enthalpy can be expressed as:
dh = du + PdV + VdP.
3. Substituting for du: Utilizing the first law,
du = Tds + PdV, we can substitute this into the enthalpy equation.
4. Rearranging Terms: After substituting and simplifying, we arrive at:
Tds = dh - VdP.
Conclusion
This expression succinctly captures the relationship between changes in entropy, enthalpy, and pressure in a thermodynamic system. Thus, option 'A' is indeed the correct expression, demonstrating a fundamental concept in mechanical engineering thermodynamics.
In thermodynamics, Tds (where T is temperature and ds is the change in entropy) is a fundamental expression that relates various state functions. To understand why option 'A' (Tds = dh - VdP) is correct, we need to explore the relationships between enthalpy (h), pressure (P), and volume (V).
Key Thermodynamic Definitions
- Enthalpy (h): Defined as h = u + Pv, where u is internal energy and Pv is the pressure-volume work.
- Entropy Change (ds): This represents the change in the disorder or randomness of a system.
Using the First Law of Thermodynamics
- The first law connects changes in internal energy (du), heat added (Q), and work done (W):
du = dQ - dW.
- For a reversible process, the heat transfer can be expressed as Tds.
Derivation of Tds = dh - VdP
1. Starting Point: Begin with the first law in differential form.
2. Enthalpy Differential: The differential of enthalpy can be expressed as:
dh = du + PdV + VdP.
3. Substituting for du: Utilizing the first law,
du = Tds + PdV, we can substitute this into the enthalpy equation.
4. Rearranging Terms: After substituting and simplifying, we arrive at:
Tds = dh - VdP.
Conclusion
This expression succinctly captures the relationship between changes in entropy, enthalpy, and pressure in a thermodynamic system. Thus, option 'A' is indeed the correct expression, demonstrating a fundamental concept in mechanical engineering thermodynamics.
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Question Description
Which one of the following expression is true for Tds equal toa)dh - VdPb)dh + VdPc)dh - PdVd)dh + PdCorrect answer is option 'A'. 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 Which one of the following expression is true for Tds equal toa)dh - VdPb)dh + VdPc)dh - PdVd)dh + PdCorrect answer is option 'A'. 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 Which one of the following expression is true for Tds equal toa)dh - VdPb)dh + VdPc)dh - PdVd)dh + PdCorrect answer is option 'A'. Can you explain this answer?.
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