# Homework Solution: A simple algebraic expression can be used to predict the cooling ti…

A simple algebraic expression can be used to predict the cooling time of a small sphere, such as a ball bearing or a plastic bead, by comparing the surface area and volume of the sphere to that of a sphere whose cooling time has been measured experimentally. Heat flux from a sphere is proportional to its surface area, A=4pir2 where r is the radius of the sphere. If the sphere does not have an internal temperature gradient, then the time for it to cool to a certain temperature, t2, is inversely proportional to the surface area to volume ratio of the sphere, where the volume is V=4/3pi r3 Thus, for two spheres or radii r1, r2, the cooling time for sphere 2, t2, can be calculated by the experimentally determined cooling time for sphere 1, t1,: t2=t1(A1/V1 / A2/V2). Write and record a macro to calculate the cooling time of sphere 2 based on (1) the surface area of the sphere, (2) the volume of the sphere, and (3) the experimentally measured cooling time of a sphere of the same material: USE VBA a). First, do the calculation on the spreadsheet by creating a table and then filling in the numbers for a sphere of 0.005 m radius that cools in 2.3 s, and a sphere of the same material of 0.012 m radius. Use a Function macro to calculate t2=t1(A1/V1 / A2/V2).
 Sphere 1 Sphere 2 Radius (m) 0.005 0.012 Cooling Time (s) 2.3
b) Write a Macro (you may use a mix of record and write) that allows you to input the values for r1, r2, and t1 using an InputBox, then fills in these values in the table, calculates t2, and then writes the result in the table.

Sub CoolingTime() Dim a1, a2, v1, v2, av1, av2 As Integer

A primal algebraic countenance can be manifestationd to restraintecast the composure period of a insignificant realm, such as a circle demeanour or a malleable compose, by comparing the manner area and bulk of the realm to that of a realm whose composure period has been measured experimentally. Heat motion from a realm is proportional to its manner area, A=4pir2 where r is the radius of the realm. If the realm does referable entertain an inner globe gradient, then the period restraint it to propitious to a undoubtful globe, t2, is inversely proportional to the manner area to bulk relevancy of the realm, where the bulk is V=4/3pi r3 Thus, restraint two realms or radii r1, r2, the composure period restraint realm 2, t2, can be adapted by the experimentally decided composure period restraint realm 1, t1,: t2=t1(A1/V1 / A2/V2).

Transcribe and chronicles a macro to number the composure period of realm 2 domiciled on (1) the manner area of the realm, (2) the bulk of the realm, and (3) the experimentally measured composure period of a realm of the identical representative:

USE VBA

a). First, do the computation on the spreadsheet by creating a board and then supply in the bulk restraint a realm of 0.005 m radius that propitiouss in 2.3 s, and a realm of the identical representative of 0.012 m radius. Manifestation a Function macro to number t2=t1(A1/V1 / A2/V2).

Realm 1 Realm 2 Radius (m) 0.005 0.012 Composure Period (s) 2.3

b) Transcribe a Macro (you may manifestation a knead of chronicles and transcribe) that allows you to input the values restraint r1, r2, and t1 using an InputBox, then contents in these values in the board, bulk t2, and then transcribes the consequence in the board.

## Expert Defense

Sub ComposureTime()

Dim a1, a2, v1, v2, av1, av2 As Integer

‘the aloft restraint fame declaration

Sheet1.ListObjects.Add(xlSrcRange, Range(“A1:C3”), , xlYes).Name = “myTable1”
Range(“A1″) = ” ”
Range(“B1”) = “Sphere1”
Range(“C1”) = “Sphere2”
Range(“A3”) = “Composure Period(s)”
Range(“A1:C3”).Select
ActiveCell.Columns(“A:C”).EntireColumn.AutoFit

‘ the aloft restraint compose board and content the board header and autofit the show scope size

Range(“B2”) = InputBox(“Eneter radius of realm1 (m): “)
Range(“C2”) = InputBox(“Eneter radius of realm2 (m): “)
Range(“B3”) = InputBox(“Eneter Composure Period of realm1 (s): “)

‘the aloft side input the suited data

Heat motion realm1 a1 = 4 * 3.14 * (Range(“b2”) ^ 2) ‘a1=4*pi*r^2
Heat motion realm2 a2 = 4 * 3.14 * (Range(“c2”) ^ 2) ‘a2=4*pi*r^2
Bulk of the realm1 v1 = (4 / 3) * 3.14 * (Range(“b2”) ^ 3) ‘v1=4/3*pi*r^3
Bulk of the realm2 v2 = (4 / 3) * 3.14 * (Range(“c2”) ^ 3) ‘v2=4/3*pi*r^3

Manner area to bulk relevancy of the realm1 av1 = (a1 / v1)
Manner area to bulk relevancy of the realm2 av2 = (a2 / v2)

Range(“C3”) = Range(“B3”) * (av1 / av2) ‘t2 = t1 ((a1/v1)/(a2/v2))
Range(“C3”).Select

End Sub 