Two identical solid blocks of the same material, one initially at a higher tempe

Question

Two identical solid blocks of the same material, one initially at a higher temperature than the other, come into contact and exchange heat, reaching thermal equilibrium at a temperature approximately halfway between the starting temperatures (GKFD Figure 5.1). The pressure on the blocks remains constant at 1 atm throughout this process. Assuming heat flows only between the two blocks, the enthalpy change for the system (i.e. the two blocks) will be zero; but the entropy of one block will rise, while the entropy of the other block will decrease.

?S=nCp ln(Tf /Ti)

(using molar heat capacity cP and n as the number of moles of material in each block, or the equivalent version for mass m and specific heat cs) to compute the entropy change for the system during this process. By

Explanation / Answer

The material of choice is Aluminium. Assume each block contains 1 mole and its molar heat capacity is 24.20 J/mol-K

deltaS for hot block = 1*24.20*ln(323/303) = 1.547 J/K

deltaS for cold block = 1*24*ln(303/283) = 1.652 J/K

entropy of mixing = -2*R(0.5ln0.5 + 0.5ln0.5) => -2*8.314*ln0.5 = +11.526

Therefore, total entropy change = 14.725 J/K

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