Doubling Volume and Number of Particles in a Thermodynamic System

In a thermodynamic system, if the volume and number of particles are doubled, we need to determine which of the following quantities is bound to be doubled:
a) Pressure
b) Temperature
c) Entropy
d) Chemical potential

To understand the effect of doubling the volume and number of particles on these quantities, let's analyze each option separately.

Pressure:
Doubling the volume and number of particles does not necessarily result in a doubling of pressure. Pressure is defined as force per unit area and is influenced by factors such as the force exerted by the particles and the frequency of collisions with the container walls. Doubling the number of particles would increase the force exerted on the walls, but doubling the volume would decrease the frequency of collisions. Therefore, it is not guaranteed that the pressure will be doubled in this scenario.

Temperature:
Doubling the volume and number of particles does not directly affect the temperature. Temperature is a measure of the average kinetic energy of the particles in a system. Doubling the volume while keeping the number of particles constant would result in a decrease in temperature, as the particles would have more space to move around. However, doubling both the volume and the number of particles would not necessarily result in a doubling of temperature.

Chemical potential:
The chemical potential is a thermodynamic quantity that determines the direction of particle flow in a system. Doubling the volume and number of particles does not necessarily result in a doubling of the chemical potential. The chemical potential depends on factors such as the type of particles, their interactions, and the temperature of the system.

Entropy:
Entropy is a measure of the disorder or randomness in a system. Doubling the volume and number of particles in a thermodynamic system is likely to increase the entropy. When the volume and number of particles are doubled, the system has more possible microstates, leading to increased disorder and higher entropy. Therefore, in this scenario, the quantity that is bound to be doubled is entropy.

In conclusion, when the volume and number of particles in a thermodynamic system are doubled, the quantity that is bound to be doubled is entropy (option c).