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Chapter 4: Q23DQ (page 713)

The air temperature and the velocity of the air have different values at different places in the earth鈥檚 atmosphere. Is theair velocity a vector field? Why or why not?Is the air temperature a vector field? Again,why or why not?

Short Answer

Expert verified

The air velocity is a vector field but the air temperature is not a vector field.

Step by step solution

01

Definition of the vector field

A vector field is a subset of space in which each point is assigned a vector.

A vector field inside the plane, for example, might be represented as a set of arrows, each with a certain speed and phase, each tied to a selected spot in the plane.

02

Describe the air velocity is a vector field

The field is having a value and a direction and these value and direction could differ at many points of space.

Is the air velocity have a value and a direction?

The answer is yes.

The air velocity must have a distinct direction at some point in Earth's atmosphere and another distinct direction at another point. And the air velocity value (speed) differs at any point in Earth's atmosphere as well.

Hence, the air velocity is a vector field.

03

Describe the air temperature is a vector field

Is air temperature have value and direction?

The answer is yes.

It has a value but it hasn't a direction. Air temperature is a scalar quantity.

Therefore, no, air temperature is not avectorfield.

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