Discussion on Fourier’s law, 11 years of professional knowledge 67
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67. The formula for Fourier’s law is Q = -λAdt/dx. Which of the following statements regarding the meaning of this formula are incorrect? The negative sign in equation (A) indicates that heat transfer occurs from the lower temperature to the higher temperature. A larger value of λ in (B) means that the material is less capable of conducting heat. dt/dx represents the temperature gradient, indicating the rate of change of temperature along the direction of heat conduction. When dt/dx is negative, it indicates that the direction of heat transfer is toward the positive x-direction; the heat quantity is positive. D represents the amount of heat transferred per unit time, while A is the area through which heat is transferred, parallel to the direction of heat transfer. In option C, it seems that the direction of heat transfer is in the negative x-direction, but the definition of temperature gradient is that the positive direction is the one in which the temperature increases. I would appreciate your advice.
I think ABC should be chosen; D is the correct one
OP, is there a standard answer?
A is wrong; as we all know, it’s from high temperature to low temperature. B is wrong; the larger it is, the easier it is. C must be wrong too – can dt/dx have positive or negative values? D is wrong; it’s the area perpendicular to the heat transfer direction
Option C is correct: when the direction of heat transfer is toward the positive x-direction, dt is negative; the heat transfer direction is the same as the x-direction
Isn’t the direction of temperature increase, which is not due to a temperature gradient, the positive direction?
What is the positive direction of X? ? ?