Question

The third law of thermodynamics states that in the limit \( T \to 0 \)?

• A. \( U = 0 \)
• B. \( S = 0 \)
• C. \( H = 0 \)
• D. \( G = 0 \)

Hint:

The third law of thermodynamics tells us that the entropy of a perfect crystal tends to zero as the temperature approaches absolute zero. This implies perfect order in the system at \( T = 0 \).

Answer 1

The Correct Option is B

The third law of thermodynamics states that as the temperature \( T \) approaches absolute zero (\( T \to 0 \)), the entropy (\( S \)) of a perfect crystal approaches zero. In other words, at absolute zero, the system is in its ground state, and there is no randomness or disorder left in the system. This is because the crystal structure is perfectly ordered at zero temperature.
Mathematically, the third law of thermodynamics is often expressed as: \[ S \to 0 {as} T \to 0 \] This statement implies that the entropy \( S \) is zero for a perfect crystal at absolute zero temperature. The other quantities mentioned in the options are not directly related to the third law:
- U (internal energy) does not necessarily go to zero at \( T = 0 \); it depends on the specific system.
- H (enthalpy) is related to both internal energy and pressure-volume work, and it does not necessarily go to zero at absolute zero.
- G (Gibbs free energy) is also not required to be zero at absolute zero according to the third law of thermodynamics.
Therefore, the correct answer is that the third law of thermodynamics states that entropy \( S = 0 \) as \( T \to 0 \).