Entropy: Why & How Does C_V Go to Zero?

[matematikuvol]

Entropy is defined by:

$$S(A)=\int^{T_A}_0C_V\frac{dT}{T}$$

where $$A$$ is state of the system in which temperature is $$T_A$$. When $$T_A\rightarrow 0$$ and $$C_V$$ must go to zero. Why? And how fast does it go?

 

[Mitadru Banik]

Your question is technically right but entropy is always increasing so it never be fall in zero.The 2nd law of thermodynamics says that (ds/dt)≥ 0. But may be in some special cases if externally keep the temperature very low depends on the state of the system its true and this is a very speedy process that is no interaction between the system and its surroundings so that the temperature is nearly= 0 and Cv falls into zero...