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The temperature distribution, at a certain instant of time in a concrete slab during curing is given by T = 3x2 + 3x + 16, where x is in cm and T is in K. The rate of change of temperature with time is given by (assume thermal diffusivity of concrete to be 0.0003 cm2/s).
- a)+0.0009 K/s
- b)+0.00048 K/s
- c)-0.00012 K/s
- d)+0.0018 K/s
Correct answer is option 'D'. Can you explain this answer?
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The temperature distribution, at a certain instant of time in a concr...
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By general heat conduction equation for 1-D heat conduction and without heat generation in Cartesian coordinates
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Solution:
Given:
Temperature distribution in the concrete slab during curing: T = 3x^2 - 3x + 16 (in K)
Thermal diffusivity of concrete: α = 0.0003 cm^2/s
To find the rate of change of temperature with time, we can use the heat conduction equation:
∂T/∂t = α * (∂^2T/∂x^2)
where ∂T/∂t is the rate of change of temperature with time, α is the thermal diffusivity, and (∂^2T/∂x^2) is the second derivative of temperature with respect to position.
Let's first find the second derivative of temperature with respect to position (∂^2T/∂x^2):
∂^2T/∂x^2 = 6
Now, substitute this value into the heat conduction equation:
∂T/∂t = α * (∂^2T/∂x^2)
∂T/∂t = 0.0003 * 6
∂T/∂t = 0.0018 K/s
Therefore, the rate of change of temperature with time is 0.0018 K/s, which corresponds to option D.
Given:
Temperature distribution in the concrete slab during curing: T = 3x^2 - 3x + 16 (in K)
Thermal diffusivity of concrete: α = 0.0003 cm^2/s
To find the rate of change of temperature with time, we can use the heat conduction equation:
∂T/∂t = α * (∂^2T/∂x^2)
where ∂T/∂t is the rate of change of temperature with time, α is the thermal diffusivity, and (∂^2T/∂x^2) is the second derivative of temperature with respect to position.
Let's first find the second derivative of temperature with respect to position (∂^2T/∂x^2):
∂^2T/∂x^2 = 6
Now, substitute this value into the heat conduction equation:
∂T/∂t = α * (∂^2T/∂x^2)
∂T/∂t = 0.0003 * 6
∂T/∂t = 0.0018 K/s
Therefore, the rate of change of temperature with time is 0.0018 K/s, which corresponds to option D.
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The temperature distribution, at a certain instant of time in a concrete slab during curing is given by T = 3x2 + 3x + 16, where x is in cm and T is in K. The rate of change of temperature with time is given by (assume thermal diffusivity of concrete to be 0.0003 cm2/s).a) +0.0009 K/sb) +0.00048 K/sc) -0.00012 K/sd) +0.0018 K/sCorrect answer is option 'D'. Can you explain this answer?
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The temperature distribution, at a certain instant of time in a concrete slab during curing is given by T = 3x2 + 3x + 16, where x is in cm and T is in K. The rate of change of temperature with time is given by (assume thermal diffusivity of concrete to be 0.0003 cm2/s).a) +0.0009 K/sb) +0.00048 K/sc) -0.00012 K/sd) +0.0018 K/sCorrect answer is option 'D'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about The temperature distribution, at a certain instant of time in a concrete slab during curing is given by T = 3x2 + 3x + 16, where x is in cm and T is in K. The rate of change of temperature with time is given by (assume thermal diffusivity of concrete to be 0.0003 cm2/s).a) +0.0009 K/sb) +0.00048 K/sc) -0.00012 K/sd) +0.0018 K/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The temperature distribution, at a certain instant of time in a concrete slab during curing is given by T = 3x2 + 3x + 16, where x is in cm and T is in K. The rate of change of temperature with time is given by (assume thermal diffusivity of concrete to be 0.0003 cm2/s).a) +0.0009 K/sb) +0.00048 K/sc) -0.00012 K/sd) +0.0018 K/sCorrect answer is option 'D'. Can you explain this answer?.
The temperature distribution, at a certain instant of time in a concrete slab during curing is given by T = 3x2 + 3x + 16, where x is in cm and T is in K. The rate of change of temperature with time is given by (assume thermal diffusivity of concrete to be 0.0003 cm2/s).a) +0.0009 K/sb) +0.00048 K/sc) -0.00012 K/sd) +0.0018 K/sCorrect answer is option 'D'. Can you explain this answer? for Chemical Engineering 2024 is part of Chemical Engineering preparation. The Question and answers have been prepared according to the Chemical Engineering exam syllabus. Information about The temperature distribution, at a certain instant of time in a concrete slab during curing is given by T = 3x2 + 3x + 16, where x is in cm and T is in K. The rate of change of temperature with time is given by (assume thermal diffusivity of concrete to be 0.0003 cm2/s).a) +0.0009 K/sb) +0.00048 K/sc) -0.00012 K/sd) +0.0018 K/sCorrect answer is option 'D'. Can you explain this answer? covers all topics & solutions for Chemical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for The temperature distribution, at a certain instant of time in a concrete slab during curing is given by T = 3x2 + 3x + 16, where x is in cm and T is in K. The rate of change of temperature with time is given by (assume thermal diffusivity of concrete to be 0.0003 cm2/s).a) +0.0009 K/sb) +0.00048 K/sc) -0.00012 K/sd) +0.0018 K/sCorrect answer is option 'D'. Can you explain this answer?.
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