What is the relationship between the heat transfer coefficient, h, and the slope, M, of the line in a semi-log plot?
Understand the Problem
The question is asking for the relationship between the heat transfer coefficient and the slope of a line in a semi-logarithmic plot, which relates to concepts in thermodynamics and heat transfer.
Answer
The slope, M, in a semi-log plot is proportional to the heat transfer coefficient, h, where M = hA/mC.
The heat transfer coefficient, h, can be determined from the initial slope, M, of the line in a semi-log plot, where it relates to the equation ln(T-T∞) = -(hA/mC)t. Here, M correlates with hA/mC.
Answer for screen readers
The heat transfer coefficient, h, can be determined from the initial slope, M, of the line in a semi-log plot, where it relates to the equation ln(T-T∞) = -(hA/mC)t. Here, M correlates with hA/mC.
More Information
In heat transfer experiments, plotting a semi-log graph of ln(T-T∞) versus time can help identify the heat transfer coefficient. The equation transformation shows that the slope of this line can reveal the coefficient when system parameters such as area, mass, and specific heat are known.
Tips
A common mistake is confusing the slope of a semi-log plot with a regular linear plot. It is critical to ensure the correct transformation of the equation for accurate slope determination.
Sources
- Solved 4. Plot equation (4) - Chegg.com - chegg.com
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