Contents

• Downloadable Microsoftâ Excel 97 worksheet (needs MS Office 97 or later).
• Spreadsheet programming; should be directly applicable to most worksheet products, e.g. MicrosoftâWorks, Lotusâ 1-2-3.
• FORTRAN code
• Graphing Calculators
• Help with Texas Instruments' programmable calculators.
• Help with Casio's programmable calculators.

Spreadsheet Programming:

Formulas used to calculate the sample results shown above:
 

Row/column	A	B	C	D	E	F	G	H	I	J	K
10						delta-t	1			Difference between
11	Radiative Cooling			Exact Soln			Approx Soln			Approx-Exact
12	Initial Temp	100		time	Temp		time	Temp		=G12	diff
13	Room Temp	20		0	=$B$13+($B$12-$B$13)*EXP(-$B$14*D13)		0	=$B$12		=G13	=H13-E13
14	a	0.1		=D13+G$10	=$B$13+($B$12-$B$13)*EXP(-$B$14*D14)		=G13+G$10	=H13-$B$14*(H13-$B$13)*G$10		=G14	=H14-E14
15				=D14+G$10	=$B$13+($B$12-$B$13)*EXP(-$B$14*D15)		=G14+G$10	=H14-$B$14*(H14-$B$13)*G$10		=G15	=H15-E15

FORTRAN code:

    Program Coffee
c
c
    open(11,file=*’/coffee-approx’, form=’formatted’)
    open(12,file=*’/coffee-exact’, form=’formatted’)
c
    call dummy
c
    nmx=14
    a= .1
c   a=.3
    dt = 1.
    troom = 20.
    tinitial = 100.
c
    ti = 100.
    t = 0.
    do n = 1,nmx
        t = t + dt
        tf = ti – a*(ti-troom)*dt
            write(6,100) t,tf
            write (11,100) t,tf
        ti = tf
    enddo
c
    write (6,101)
c
    ti = 100.
    t = 0.
    do n=l,nmx
        t = t + dt
        tf = troom + (tinitial – troom)*exp(-a*t)
            write (6,100) t,tf
            write (12,100) t,tf
        ti = tf
    enddo
c
 100 format (f7.0,f9.1)
 101 format (/)
    stop
    end