The Calculator Minimalist Programming Club

[Thomas Klemm]

(03-03-2019 11:55 AM)Csaba Tizedes Wrote:  One application on my TI-57 LCD - maybe it is enough for membership:
TI 57 LCD calculator solves Clausius Clapeyron with Euler method

For those interested here's the program for the TI-57II:

Code:

LBL 0   23.00     00
RCL 0   71.00     01
÷       55        02
RCL 1   71.01     03
x²      34        04
×       65        05
RCL 2   71.02     06
×       65        07
RCL 3   71.03     08
=       95        09
STO+ 0  61.85.00  10
RCL 3   71.03     11
STO+ 1  61.85.01  12
RCL 0   71.00     13
x<t    -27        14
GTO 0   22.00     15
Pause   96        16
RCL 1   71.01     17
–       75        18
RCL 3   71.03     19
÷       55        20
2       02        21
=       95        22
R/S     13        23

We can solve this differential equation by separating the variables:

\(\int_{p_0}^{p_b} \frac{dp}{p}=C \int_{T_0}^{T_b} \frac{dT}{T^2}\)

This leads to:

\(\log(p_b) - \log(p_0) = C \left (\frac{1}{T_0} - \frac{1}{T_b} \right )\)

Which allows us to solve for \(T_b\):

\(\begin{align*}
\frac{1}{T_b} &= \frac{1}{T_0} - \frac{\log(p_b) - \log(p_0)}{C} \\
&= \frac{1}{T_0} + \frac{\log(p_0) - \log(p_b)}{C} \\
&= \frac{1}{T_0} + \frac{\log(\frac{p_0}{p_b})}{C} \\
\end{align*}\)

Given the following values we can calculate the temperature \(t_b = T_b - 273.15\) of the boiling point:

\(\begin{matrix}
T_0 =&100 + 273.15 \\
p_0 =&101325 \\
p_b =&200000\\
C =& 4889
\end{matrix}\)

100 + 273.15 =
1/x + (101325 ÷ 200000) lnx ÷ 4889 =
1/x - 273.15 =
120.42637

Cheers
Thomas

[Csaba Tizedes]

(03-03-2019 04:27 PM)Thomas Klemm Wrote:  ...here's the program...

Thank you for typing!

(03-03-2019 04:27 PM)Thomas Klemm Wrote:  We can solve this differential equation by separating the variables...t=120.42637

Yes, and here my CASIO fx-991DEX with SOLVE+integral solves the same problem:



SOLVE+integral really useful in this case.

Csaba

[Harald]

(01-16-2017 04:59 PM)Eddie W. Shore Wrote:  Looking at picture of Sinclair Cambridge Scientific (thanks Google), and if I extended the Minimalist club to include non-programmable scientific calculators, this would definitely qualify.

How about the Sinclair Scientific Programmable?

[Dave Britten]

(03-06-2019 01:26 PM)Harald Wrote:  

(01-16-2017 04:59 PM)Eddie W. Shore Wrote:  Looking at picture of Sinclair Cambridge Scientific (thanks Google), and if I extended the Minimalist club to include non-programmable scientific calculators, this would definitely qualify.

How about the Sinclair Scientific Programmable?

If that's anything like the Sinclair Cambridge Programmable, then it's a tremendous challenge to do anything particularly useful with its 36 steps and one storage register.

[Harald]

(03-06-2019 05:50 PM)Dave Britten Wrote:  

(03-06-2019 01:26 PM)Harald Wrote:  How about the Sinclair Scientific Programmable?

If that's anything like the Sinclair Cambridge Programmable, then it's a tremendous challenge to do anything particularly useful with its 36 steps and one storage register.

Yes, it even is a challange to do simple calculations. But the program library is pretty impressive. It is amazing how much they acomplished with the limited resources this calculator has.

Cheers,
Harald

[EdS2]

There's a workalike model of Sinclair's Cambridge Programmable to run in your browser here. This machine has a conditional branch, so it really is programmable, whereas their earlier Scientific Programmable could only record keystroke sequences. I'd be very interested to see the program library for the Cambridge Programmable. (Katie's site has only the 10 page sample.)