Question

A: Entropy of a perfect crystalline solid at absolute zero approaches zero.
B: For spontaneity of a reaction, T\(\Delta\)S>\(\Delta\)H.
Among the two statements given above, identify the correct answer from the options given below.

• A. Both 'A' and 'B' are true
• B. 'A' is true but 'B' is false
• C. Both 'A' and 'B' are false
• D. 'A' is false but 'B' is true

Hint:

Remember the key thermodynamic principles:

• \textbf{Third Law:} S \(\rightarrow\) 0 as T \(\rightarrow\) 0 K for a perfect crystal.
• \textbf{Spontaneity (Gibbs Free Energy):} A reaction is spontaneous if \(\Delta\)G<0. Always start from the fundamental equation \(\Delta G = \Delta H - T\Delta S\) to derive the conditions for spontaneity.

Answer 1

The Correct Option is A

Step 1: Analyzing Statement A.
Statement A says, "Entropy of a perfect crystalline solid at absolute zero approaches zero." This is a direct statement of the Third Law of Thermodynamics. The law states that as the temperature of a system approaches absolute zero (0 K), the entropy of the system approaches a minimum value. For a perfect crystalline substance, this minimum entropy is zero, as there is only one possible arrangement of atoms (one microstate, W=1, and S = k ln W = 0). Therefore, Statement A is true.
Step 2: Analyzing Statement B.
Statement B gives a condition for the spontaneity of a reaction: T\(\Delta\)S>\(\Delta\)H. The spontaneity of a process at constant temperature and pressure is determined by the change in Gibbs free energy (\(\Delta\)G). The relationship is: \[ \Delta G = \Delta H - T\Delta S \] For a process to be spontaneous, the change in Gibbs free energy must be negative (\(\Delta\)G<0). So, for spontaneity: \[ \Delta H - T\Delta S<0 \] Rearranging this inequality: \[ \Delta H<T\Delta S \] or \[ T\Delta S>\Delta H \] This exactly matches the condition given in Statement B. Therefore, Statement B is true.
Step 3: Final Answer.
Both statements A and B are true.