3. consider the following 'experiment'. a beaker containing 1000 black beads and 1000 white beads is mixed. the beads are identical except for their c colour. the potential energy of the beads on the

The mixing of 1000 black beads and 1000 white beads, where the potential energy and enthalpy change are zero, can be explained as spontaneous due to an increase in entropy. Entropy is a measure of disorder or randomness in a system. Before mixing, the beads are more ordered (separated by color), which is a state of lower entropy. When the beads are mixed, the number of possible arrangements (microstates) increases significantly, leading to an increase in entropy. Even though there is no change in enthalpy (heat content), the increase in entropy favors the mixing process because systems tend to evolve towards states with higher entropy, making the mixing spontaneous. This entropy-driven spontaneous mixing results from the increased number of ways the beads can be arranged when mixed compared to when segregated. Thus, the spontaneous mixing is driven by the increase in entropy, not by changes in enthalpy or potential energy, illustrating the fundamental thermodynamic principle that processes which increase the total entropy of the system and its surroundings tend to occur spontaneously.