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Amount of Out-Gassed Mass due to Diffusion,Total Mass Loss (TML)

Calculate the amount of mass that will be out-gassed each day during the first week on orbit by a 10 kg source with Ea = 10 kcal/mole that meets the ASTM E 595 requirements and is held at a temperature T. The ASTM E595 requirement is that a surface at T = 125 C and a pressure less than 7e-3 Pa during 24 hours should have a Total Mass Loss (TML) less than 1%. Given:

clc; clear all;
Ea = 10;            % Ea is the activation energy [kcal/mole]
R  = 1.9859e-3;     % R is the gas constant [kcal mole-1 K-1]
M  = 12;            % Source Mase [kg]
Days = 7;           % Out-gassing interval [day]
dm = 0.01*M;                  % Allowed Total Mass Loss[kg]
Ts  = 125 + 273.15 ;          % [K]
% q0 - describes the specific out-gassing characteristics of the material
q0 = dm/(2*exp(-Ea/(R*Ts)));  % [kg/day^0.5]

Find the amount of mass out-gassed between time t1 and t2

T = [0,25,50,75,100,125];
dm = zeros(7,6);
fprintf('Amount of mass out-gassed each day during a week, M_i = 12kg\n\n');
fprintf('Day  %4d   %4d    %4d     %4d     %4d     %4d [C] \n',T);
T = T + 273.15; % [K]
for i = 1:Days
    dm(i,:) = q0*(2*exp(-Ea./(R*T)))*(i^0.5-(i -1)^0.5)*1e3; %[g]
   fprintf([num2str(i),'     %4.3f  %4.3f   %4.3f   %4.3f   %4.3f    %4.3f \n'],(dm(i,:)));
end
Amount of mass out-gassed each day during a week, M_i = 12kg

Day     0     25      50       75      100      125 [C] 
1     0.368  1.726   6.374   19.514   51.427    120.000 
2     0.152  0.715   2.640   8.083   21.302    49.706 
3     0.117  0.548   2.026   6.202   16.345    38.140 
4     0.099  0.462   1.708   5.229   13.780    32.154 
5     0.087  0.407   1.505   4.607   12.140    28.328 
6     0.078  0.368   1.360   4.165   10.976    25.611 
7     0.072  0.339   1.251   3.830   10.093    23.551
figure(1);
semilogy(dm);
hold on;
semilogy(dm,'*');
title('Amount of mass out-gassed each day during a week, M_i = 12kg');
legend('0 C^o','25 C^o','50 C^o','75 C^o','100 C^o','125 C^o');
xlabel('Days');
ylabel('Out-gassed mass[g]');

Out_gassed_mass

 

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