Final answer:
Entropy increases during an isochoric process because the system, which is heated at constant volume, gains kinetic energy, resulting in more microstates and hence greater disorder. The second law of thermodynamics states that in any natural process, the total entropy either increases or remains constant; it never decreases. An isochoric process is typically irreversible, leading to an increase in entropy as the system is heated.
Step-by-step explanation:
You have observed that entropy increases with an increase in temperature and typically decreases with an increase in pressure.
However, in an isochoric process, where the volume is constant, temperature and pressure both change such that temperature increases while pressure remains constant, as no work is done on or by the system.
This specific process can lead to general confusion since entropy is oftentimes discussed in terms of processes involving both volume and pressure changes.
When analyzing the relationship between entropy and pressure at constant volume, it's critical to understand that entropy, fundamentally, is related to the number of microstates available to a system, which is a measure of disorder or randomness.
When heating a gas at constant volume, you increase the kinetic energy of the gas particles, which translates to an increased number of microstates due to higher particle speeds and more potential particle positions at every instant in time. This increase in the number of microstates results in an increase in entropy.
During an isochoric process, there is no volume change, so there is no work done, which implies that any heat transfer into the system increases the internal energy and, hence, the temperature of the system.
According to the second law of thermodynamics, the total entropy of a system either increases or remains constant in any natural process; it never decreases.
Therefore, in an isochoric heating process, entropy increases because the system is gaining heat, and the temperature increases without work being done, making the process irreversible under natural conditions and leading to an increase in entropy.