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During an adiabatic process the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of Cp /cv for the gas is... (a) 4/3 (b) 2 (c) 5/3 (d) 3/2
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During an adiabatic process the pressure of a gas is found to be propo...
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During an adiabatic process the pressure of a gas is found to be propo...
Understanding the Problem
In an adiabatic process, the relationship between pressure (P) and temperature (T) is given as P ∝ T³. We need to find the ratio of specific heats, Cp/Cv, for the gas.
Adiabatic Relations
For an ideal gas undergoing an adiabatic process, the following relationship holds:
- P * V^γ = constant, where γ = Cp/Cv.
Using the given relationship P ∝ T³, we can express this as:
- P = k * T³ (where k is a constant)
Using Ideal Gas Law
From the ideal gas law (PV = nRT), we can relate pressure and temperature:
- V = nRT/P
Substituting P = kT³ into the ideal gas law gives us:
- V = nRT/(kT³) = nR/(kT²)
Relating V and T
In an adiabatic process, we also have the relationship:
- T * V^(γ-1) = constant.
Substituting V from the previous equation into this relation:
- T * (nR/(kT²))^(γ-1) = constant.
This leads us to the conclusion that γ must equal 4/3 to satisfy the proportional relationship derived earlier.
Conclusion
Thus, we find that the ratio of specific heats for the gas is:
- Cp/Cv = γ = 4/3.
The correct answer is (a) 4/3.
In an adiabatic process, the relationship between pressure (P) and temperature (T) is given as P ∝ T³. We need to find the ratio of specific heats, Cp/Cv, for the gas.
Adiabatic Relations
For an ideal gas undergoing an adiabatic process, the following relationship holds:
- P * V^γ = constant, where γ = Cp/Cv.
Using the given relationship P ∝ T³, we can express this as:
- P = k * T³ (where k is a constant)
Using Ideal Gas Law
From the ideal gas law (PV = nRT), we can relate pressure and temperature:
- V = nRT/P
Substituting P = kT³ into the ideal gas law gives us:
- V = nRT/(kT³) = nR/(kT²)
Relating V and T
In an adiabatic process, we also have the relationship:
- T * V^(γ-1) = constant.
Substituting V from the previous equation into this relation:
- T * (nR/(kT²))^(γ-1) = constant.
This leads us to the conclusion that γ must equal 4/3 to satisfy the proportional relationship derived earlier.
Conclusion
Thus, we find that the ratio of specific heats for the gas is:
- Cp/Cv = γ = 4/3.
The correct answer is (a) 4/3.
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During an adiabatic process the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of Cp /cv for the gas is... (a) 4/3 (b) 2 (c) 5/3 (d) 3/2
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During an adiabatic process the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of Cp /cv for the gas is... (a) 4/3 (b) 2 (c) 5/3 (d) 3/2 for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about During an adiabatic process the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of Cp /cv for the gas is... (a) 4/3 (b) 2 (c) 5/3 (d) 3/2 covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During an adiabatic process the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of Cp /cv for the gas is... (a) 4/3 (b) 2 (c) 5/3 (d) 3/2.
During an adiabatic process the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of Cp /cv for the gas is... (a) 4/3 (b) 2 (c) 5/3 (d) 3/2 for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about During an adiabatic process the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of Cp /cv for the gas is... (a) 4/3 (b) 2 (c) 5/3 (d) 3/2 covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for During an adiabatic process the pressure of a gas is found to be proportional to the cube of its temperature. The ratio of Cp /cv for the gas is... (a) 4/3 (b) 2 (c) 5/3 (d) 3/2.
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