An increase in entropy is related to a)expansion of a gas into a
vacuum,b) two objects coming to thermal equilibrium c) both d) none
The correct answer is c) both.
To understand why an increase in entropy is related to both an expansion of a gas into a vacuum and two objects coming to thermal equilibrium, let's first define what entropy is. Entropy is a thermodynamic property that quantifies the randomness or disorder within a system.
a) Expansion of a gas into a vacuum: When a gas expands into a vacuum, it occupies a larger volume and its molecules are more dispersed. This results in an increase in entropy because the gas molecules have more possible positions and velocities, increasing the disorder or randomness of the system.
To confirm this, you can use the ideal gas law, which states that the entropy of an ideal gas is directly proportional to its volume. As the volume increases during expansion, the entropy of the gas will also increase.
b) Two objects coming to thermal equilibrium: When two objects at different temperatures are brought into contact with each other, heat transfer occurs between them until they reach a common temperature. This process is known as thermal equilibrium. In this case, an increase in entropy is associated with achieving thermal equilibrium.
To see why, let's consider two objects: one at a higher temperature (object A) and the other at a lower temperature (object B). Initially, object A has higher energy and object B has lower energy. As heat flows from object A to object B, the energy becomes more evenly distributed between the two objects. This increase in energy distribution leads to a greater number of possible microstates, or ways in which the energy of the entire system can be distributed among its particles.
According to the statistical definition of entropy, the entropy of a system is related to the natural logarithm of the number of microstates. As the number of microstates increases during the process of reaching thermal equilibrium, the entropy of the system also increases.
Therefore, both the expansion of a gas into a vacuum and two objects coming to thermal equilibrium result in an increase in entropy.