Question

Indicate whether each statement is true or false. (a) The entropy of the universe increases for any spontaneous process. (b) The entropy change of the system is equal and opposite that of the surroundings for any irreversible process. (c) The entropy of the system must increase in any spontaneous process. (d) The entropy change for an isothermal process depends on both the absolute temperature and the amount of heat reversibly transferred.

Answer 1

(a)

Spontaneous processes are irreversible in nature. The entropy change of the system is always the same and is given as follows:

This change in entropy is always positive for a spontaneous process.

The surroundings take up heat in an irreversible manner and the entropy change is of the surroundings is less than for the system.

Entropy change of the universe is the sum of the entropy change of the system and surroundings as shown below:

Therefore, the entropy of the system always increases and the statement is true.

(b)

Entropy change of the universe is the sum of the entropy change of the system and surroundings as shown below:

The entropy of the universe for a reversible process is .

Thus, the following relation between the entropy of the system and surroundings can be obtained:

Therefore, the entropy change for the system and surroundings is equal and opposite in sign for a reversible process, but not so for an irreversible process. Hence, the given statement is false.

(c)

The Gibb’s free energy change for a process is given as follows:

For a process to be spontaneous the Gibb’s free energy change should be negative. This is possible for a process is of the process is positive, such that .

Therefore, the given statement is true.

(d)

Entropy change for an isothermal process is given as follows:

According to this expression, entropy change for the system depends both on the absolute temperature and the heat taken up by the system. Hence, the statement is true.