Question

Explain why a building made of bricks has smaller entropy than the same bricks in a disorganized pile. Do this by considering the number of ways that each could be formed (the number of microstates in each macrostate).

Short answer

The entropy of a building made of bricks is lower than that of bricks in a disorganized pile because of the lower number of microstates in a building made of bricks.

Step-by-step solution

Explain why the entropy of a building made of bricks is smaller than the same bricks in a disorganized pile.

The arrangement of bricks in a building is well structured and ordered, while this is disordered in the case of bricks in a disorganized pile. Entropy is the measure of disorder, so the bricks in disorganized pile have a higher entropy than a building made of bricks.

Explain the reason by considering the number of microstates in each macrostate.

A microstate is the arrangement of particles in a macrostate at an instant. In the case of a building made of bricks, bricks can be arranged in only a limited number of directions. So, the number of microstates is lower. But the bricks can be arranged in different directions in a disorganized pile, and this will cause more microstates.

As the number of microstates increases in a macrosystem, entropy will also increase. Because entropy in a macrostate is equal to the product of the Boltzmann constant and the natural logarithm of the number of microstates in the macrostate.

So, building made of bricks has low entropy because of the smaller number of microstates.