# 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 undesigning algebraic indication can be interpretationd to restraintebode the subsidence duration of a little region, such as a order direction or a tractile compose, by comparing the exterior area and compass of the region to that of a region whose subsidence duration has been measured experimentally. Heat progression from a region is proportional to its exterior area, A=4pir2 where r is the radius of the region. If the region does referable own an interior clime gradient, then the duration restraint it to irresolute to a infallible clime, t2, is inversely proportional to the exterior area to compass aspect of the region, where the compass is V=4/3pi r3 Thus, restraint couple regions or radii r1, r2, the subsidence duration restraint region 2, t2, can be adapted by the experimentally resolute subsidence duration restraint region 1, t1,: t2=t1(A1/V1 / A2/V2).

Transcribe and proceedings a macro to apfaction the subsidence duration of region 2 installed on (1) the exterior area of the region, (2) the compass of the region, and (3) the experimentally measured subsidence duration of a region of the corresponding esthetic:

USE VBA

a). First, do the estimation on the spreadsheet by creating a consideration and then satisfaction in the mass restraint a region of 0.005 m radius that irresolutes in 2.3 s, and a region of the corresponding esthetic of 0.012 m radius. Interpretation a Function macro to apfaction t2=t1(A1/V1 / A2/V2).

Region 1 Region 2 Radius (m) 0.005 0.012 Subsidence Duration (s) 2.3

b) Transcribe a Macro (you may interpretation a knead of proceedings and transcribe) that allows you to input the values restraint r1, r2, and t1 using an InputBox, then gluts in these values in the consideration, apportions t2, and then transcribes the conclusion in the consideration.

## Expert Confutation

Sub SubsidenceTime()

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

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

‘ the overhead restraint compose consideration and glut the consideration header and autofit the spread-out scene size

Range(“B2”) = InputBox(“Eneter radius of region1 (m): “)
Range(“C2”) = InputBox(“Eneter radius of region2 (m): “)
Range(“B3”) = InputBox(“Eneter Subsidence Duration of region1 (s): “)

‘the overhead faction input the conducive data

Heat progression region1 a1 = 4 * 3.14 * (Range(“b2”) ^ 2) ‘a1=4*pi*r^2
Heat progression region2 a2 = 4 * 3.14 * (Range(“c2”) ^ 2) ‘a2=4*pi*r^2
Compass of the region1 v1 = (4 / 3) * 3.14 * (Range(“b2”) ^ 3) ‘v1=4/3*pi*r^3
Compass of the region2 v2 = (4 / 3) * 3.14 * (Range(“c2”) ^ 3) ‘v2=4/3*pi*r^3

Exterior area to compass aspect of the region1 av1 = (a1 / v1)
Exterior area to compass aspect of the region2 av2 = (a2 / v2)

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

End Sub