Plot Specific Heat of Solids (a) Dulong-Petit law, (b) Einstein distribution function, (c) Debye

 

Plot Specific Heat of Solids (a) Dulong-Petit law, (b) Einstein distribution function, (c) Debye distribution function for high temperature and low temperature and compare them for these two cases

Program :

clf;clc
K = 1.38e-23 // Boltzmann Constant in (J/K) unit
T = linspace(0,1000,50) // Absolute temperature at K unit
theta_E = 230 // Einstein teamperature in K unit for copper
theta_D = 343 // Debye teamperature in K unit for copper
function y=DP(T) //Dulong-Petit law
y = ones(T) // Here, y = Specific Heat/3R
endfunction
plot(T,DP,'*k')
function y=E(T) //Einstein theorem
A = (T./(theta_E))
 if T == 0 then
 y = 0 // Here, y = Specific Heat/3R
else
 x = 1./A
 y = ((x^2)*exp(x))/((exp(x)-1)^2)
end
endfunction
plot(T,E,'+k')
function y=D(T) // Debye theorem
B = (T./theta_D)
 if T == 0 then
 y = 0 // Here, y = Specific Heat/3R
else
 z = B
 y = (3*(z^3))*integrate("(exp(x)*(x^4))/((exp(x)-1)^2)","x",0,1./z)
 end
endfunction
plot(T,D,'k',"linewidth",2)
legend("Dulong-Petit","Einstein","Debye",4)
xlabel("Absolute Temperature( K ) ","font_size",3)
ylabel("Specific Heat/3R","font_size",3)
title("Comparison between Specific Heat","font_size",3)
replot([0,0,1000,1.2])
xgrid
output: