Hence, the process of the gas spreading around the room is irreversible. Although it is possible that all the particles can return to the start box at the same instant, there are no laws really preventing this, only that the probability of this occurring is exceedingly small. When the perfume is released, the system of the enclosed gas spontaneously changes from a state of low probability to one of higher probability, that is, the entropy of the system increases. The relationship between probability and entropy is given by = loge( ) S k w is the entropy, is the Boltzmann constant S k and is defined as the number of w “loosely” molecular arrangements that correspond to the same macroscopic state. In our initial state (t = 0), there is only one possible arrangement of the particles all the particles must be in the start box, – = 1 = 0. w S The tells us Second Law of Thermodynamics, that if an isolated system undergoes a spontaneous process, its final state will be one in which the entropy and are maximum. S w MATLAB MSCRIPT Setup for initial position of particles in start box using the Matlab command rand to give a set of numbers between zero and one e.g. rand(1,5) 0.7612 0.7568 0.3738 0.5126 0.9739 % initial position of N particles within unit box ------------------------ R = 1; % max step length P = rand(N,2); % initial (x,y) coordinates of N particles x = P(:,1); y = P(:,2);
Hence, the process of the gas spreading around the room is irreversible. Although it is possible that all the particles can return to the start box at the same instant, there are no laws really preventing this, only that the probability of this occurring is exceedingly small. When the perfume is released, the system of the enclosed gas spontaneously changes from a state of low probability to one of higher probability, that is, the entropy of the system increases. The relationship between probability and entropy is given by S = k loge( w ) S is the entropy, k is the Boltzmann constant and w is “loosely” defined as the number of molecular arrangements that correspond to the same macroscopic state. In our initial state (t = 0), there is only one possible arrangement of the particles – all the particles must be in the start box, w = 1 S = 0. The Second Law of Thermodynamics, tells us that if an isolated system undergoes a spontaneous process, its final state will be one in which the entropy S and w are maximum. MATLAB MSCRIPT Setup for initial position of particles in start box using the Matlab command rand to give a set of numbers between zero and one e.g. rand(1,5) 0.7612 0.7568 0.3738 0.5126 0.9739 % initial position of N particles within unit box ------------------------ R = 1; % max step length P = rand(N,2); % initial (x,y) coordinates of N particles x = P(:,1); y = P(:,2);
tp_equilibrium_docx.docx