Criterion of Spontaneity in Terms of System Properties

The spontaneity of a process is determined by the properties of the system. The correct criterion of spontaneity in terms of the properties of the system alone is given by:

(dS)U, V 0

Explanation:

Entropy (S) is a measure of the disorder or randomness of a system. The change in entropy (dS) is related to the heat (q) that flows into or out of the system during a process, as well as the temperature (T) of the system. The criterion of spontaneity can be expressed in terms of the change in entropy:

(dS) q/T

For a process to be spontaneous, the change in entropy (dS) must be positive. However, the sign of q depends on the conditions of the process, such as the temperature and pressure. Therefore, the criterion of spontaneity must be expressed in terms of system properties that do not depend on the conditions of the process.

One such property is the internal energy (U) of the system, which is the sum of the kinetic and potential energies of the particles in the system. The change in internal energy (dU) is related to the heat (q) that flows into or out of the system, as well as the work (w) done on or by the system:

dU q + w

For a closed system (i.e., one that does not exchange matter with its surroundings), the work done on or by the system can be expressed in terms of the volume (V) of the system:

w -PdV

where P is the pressure.

Using these equations, the change in entropy can be expressed in terms of the internal energy and volume of the system:

(dS)U, V (dU/T) (P/T)(dV/T) 0

This criterion of spontaneity states that a process is spontaneous if the change in entropy is positive for a given internal energy and volume of the system. It does not depend on the conditions of the process, such as the temperature and pressure.

Conclusion:

The correct criterion of spontaneity in terms of the properties of the system alone is option 'A': (dS)U, V 0. This criterion states that a process is spontaneous if the change in entropy is positive for a given internal energy and volume of the system. It does not depend on the temperature and pressure of the system.