# Entropy: Why & How Does C_V Go to Zero?

• matematikuvol
In summary, entropy is defined by the equation S(A)=\int^{T_A}_0C_V\frac{dT}{T}, where A is the state of the system with temperature T_A. As T_A approaches zero, C_V must also approach zero. This is due to the second law of thermodynamics, which states that the rate of change of entropy with respect to time is always greater than or equal to zero. However, in some special cases where the system is externally kept at a very low temperature, it is possible for S(A) to be equal to zero. This is a rapid process where there is no interaction between the system and its surroundings, causing the temperature to nearly reach zero and C_V to fall 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?

Last edited:
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...

## 1. What is Entropy and why is it important in studying thermodynamics?

Entropy is a measure of the disorder or randomness in a system. In thermodynamics, it is a crucial concept as it helps us understand the direction and extent of energy flow and chemical reactions in a system. It also plays a role in determining the efficiency of energy conversion processes.

## 2. How does entropy relate to the Second Law of Thermodynamics?

The Second Law of Thermodynamics states that the total entropy of an isolated system will always increase over time. This means that as energy is transferred or transformed, the overall entropy of the system will always increase, leading to a decrease in the available energy for work.

## 3. Why does the heat capacity (CV) of a system approach zero at absolute zero temperature?

This is due to the Third Law of Thermodynamics, which states that the entropy of a perfect crystal at absolute zero temperature is zero. Since heat capacity is related to the change in entropy with temperature, at absolute zero, the change in entropy is zero and thus the heat capacity approaches zero.

## 4. Can entropy be reversed or decreased in a system?

In isolated systems, entropy cannot be reversed or decreased as it is a measure of the disorder or randomness, which naturally increases over time. However, in open systems, entropy can be reduced locally, but at the expense of an increase in entropy elsewhere in the system.

## 5. How can we use the concept of entropy to predict the direction of chemical reactions?

In a chemical reaction, the overall entropy of the system and its surroundings will always increase. This means that the reaction will spontaneously occur in the direction that leads to an increase in entropy. By calculating the change in entropy of a reaction, we can predict the direction in which the reaction will proceed.

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