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Methane diffuses at steady state through a tube containing helium. At point 1 the partial
pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total
pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the
value of diffusivity is 6.75×10–5 m2
/sec.
i) Calculate the flux of CH4 at steady state for equimolar counter diffusion
ii) Calculate the partial pressure at a point 0.02 m apart from point 1?
pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total
pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the
value of diffusivity is 6.75×10–5 m2
/sec.
i) Calculate the flux of CH4 at steady state for equimolar counter diffusion
ii) Calculate the partial pressure at a point 0.02 m apart from point 1?
Most Upvoted Answer
Methane diffuses at steady state through a tube containing helium. At ...
i) Calculate the flux of CH4 at steady state for equimolar counter diffusion
To calculate the flux of methane (CH4) at steady state, we can use Fick's first law of diffusion, which is given by:
\[ J_A = -D \cdot \frac{(P_{A2} - P_{A1})}{(x_2 - x_1)} \]
Where:
- \( J_A \) is the flux of CH4 (mol/m²·s)
- \( D \) is the diffusivity (6.75×10⁻⁵ m²/s)
- \( P_{A1} = 55 \) kPa
- \( P_{A2} = 15 \) kPa
- Distance \( (x_2 - x_1) = 0.03 \) m
Plugging in the values:
\[
J_A = -6.75 \times 10^{-5} \cdot \frac{(15 - 55)}{0.03}
\]
Calculating:
\[
J_A = -6.75 \times 10^{-5} \cdot \frac{-40}{0.03}
\]
\[
J_A = 6.75 \times 10^{-5} \cdot 1333.33 \approx 0.00009 \text{ mol/m²·s}
\]
Thus, the flux of CH4 is approximately 0.00009 mol/m²·s.
ii) Calculate the partial pressure at a point 0.02 m apart from point 1
To find the partial pressure at a point 0.02 m from point 1, we can apply a linear approximation based on Fick's law. The change in pressure can be calculated using the following relationship:
\[
\Delta P_A = J_A \cdot (x_2 - x_1)
\]
Where \( J_A \) is the flux we calculated earlier.
Substituting the values:
\[
\Delta P_A = 0.00009 \cdot 0.02
\]
Calculating:
\[
\Delta P_A \approx 0.0000018 \text{ kPa}
\]
Thus, the new partial pressure \( P_{A} \) at 0.02 m from point 1 is:
\[
P_{A} = P_{A1} - \Delta P_A
\]
\[
P_{A} = 55 - 0.0000018 \approx 55 \text{ kPa}
\]
The partial pressure at this point remains effectively 55 kPa, as the change is negligible over such a short distance.
To calculate the flux of methane (CH4) at steady state, we can use Fick's first law of diffusion, which is given by:
\[ J_A = -D \cdot \frac{(P_{A2} - P_{A1})}{(x_2 - x_1)} \]
Where:
- \( J_A \) is the flux of CH4 (mol/m²·s)
- \( D \) is the diffusivity (6.75×10⁻⁵ m²/s)
- \( P_{A1} = 55 \) kPa
- \( P_{A2} = 15 \) kPa
- Distance \( (x_2 - x_1) = 0.03 \) m
Plugging in the values:
\[
J_A = -6.75 \times 10^{-5} \cdot \frac{(15 - 55)}{0.03}
\]
Calculating:
\[
J_A = -6.75 \times 10^{-5} \cdot \frac{-40}{0.03}
\]
\[
J_A = 6.75 \times 10^{-5} \cdot 1333.33 \approx 0.00009 \text{ mol/m²·s}
\]
Thus, the flux of CH4 is approximately 0.00009 mol/m²·s.
ii) Calculate the partial pressure at a point 0.02 m apart from point 1
To find the partial pressure at a point 0.02 m from point 1, we can apply a linear approximation based on Fick's law. The change in pressure can be calculated using the following relationship:
\[
\Delta P_A = J_A \cdot (x_2 - x_1)
\]
Where \( J_A \) is the flux we calculated earlier.
Substituting the values:
\[
\Delta P_A = 0.00009 \cdot 0.02
\]
Calculating:
\[
\Delta P_A \approx 0.0000018 \text{ kPa}
\]
Thus, the new partial pressure \( P_{A} \) at 0.02 m from point 1 is:
\[
P_{A} = P_{A1} - \Delta P_A
\]
\[
P_{A} = 55 - 0.0000018 \approx 55 \text{ kPa}
\]
The partial pressure at this point remains effectively 55 kPa, as the change is negligible over such a short distance.
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Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1?
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Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1?.
Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1?.
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Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1?, a detailed solution for Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1? has been provided alongside types of Methane diffuses at steady state through a tube containing helium. At point 1 the partial pressure of methane is pA1 = 55 kPa and at point 2, 0.03 m apart pA2 = 15 kPa. The total pressure is 101.32 kPa, and the temperature is 298 K. At this pressure and temperature, the value of diffusivity is 6.75×10–5 m2 /sec. i) Calculate the flux of CH4 at steady state for equimolar counter diffusion ii) Calculate the partial pressure at a point 0.02 m apart from point 1? theory, EduRev gives you an
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