The following plot shows temperature as a function of x and y. Along which path is the temperature change minimum?
To determine along which path the temperature change is minimum, we need to analyze the given options and understand their implications on the gradient of the temperature. The gradient of a scalar field, such as temperature, points in the direction of the maximum rate of increase of the field.
1. Path: \(x = \text{constant or } y = \text{constant}\)
This implies straight lines parallel to the axes. The temperature change can be significant as there might be steep contours crossed.
2. Path: \(\frac{y}{x^2} = \text{constant}\)
This represents a parabolic path. While temperature change may vary, it is not necessarily the path of minimum change since contour curves like circles or ellipses also need to be considered.
3. Path: \(y^2 + x^2 = \text{constant}\)
This represents a circular path centered at the origin. This type of path usually represents an equipotential line where the change in temperature would be minimum because you are moving along constant temperature lines.
4. Path: \(y \cdot x = \text{constant}\)
This represents a hyperbolic path. Similar to parabolic paths, the temperature change isn't minimal as it can cut through several contours.
Based on the explanation of the paths above, the path \(y^2 + x^2 = \text{constant}\) is the correct answer. This path indicates movement along a circle which generally corresponds to paths of minimal change for fields exhibiting radial symmetry, such as temperature fields seen on typical 2D plots.
Important Questions from Data Interpetation (Notes)
- Answer the question on the basis of the informations given below :
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Which one of the following is CORRECT?The Sankey diagram shows food preferences of males and females. The widths of the bands are proportional to numbers of persons opting for a given food item.
Which one of the following is an INCORRECT statement about the food preferences?The following figure shows densities and masses of five objects (A to E).
The object with the largest volume is _____
