Helmholtz free energy question

In summary, Helmholtz free energy is a thermodynamic potential that measures the amount of work that can be extracted from a system at a constant temperature and volume. It is calculated using the equation A = U - TS and is significant in determining the maximum work that can be obtained from a system and its equilibrium conditions. It is also related to other thermodynamic potentials and is useful in situations with constant temperature and volume, such as in closed systems, and in the study of chemical reactions and phase transitions.
  • #1
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for the proof of the helmholtz free energy question,
why is q smaller or equal to T(S2-S1)?
 
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  • #2
anybody ?
 
  • #3


The proof of the Helmholtz free energy question involves examining the change in the Helmholtz free energy (F) of a system at constant temperature (T) and volume (V). This change is given by the equation ΔF = q - TΔS, where q is the heat added to the system and ΔS is the change in entropy.

In this equation, q represents the energy that is added to the system in the form of heat. This energy can come from various sources, such as thermal radiation or chemical reactions. However, it is important to note that this energy cannot be greater than the change in entropy multiplied by the temperature (TΔS).

This is because the second law of thermodynamics states that the total entropy of a closed system can never decrease. Therefore, the change in entropy (ΔS) must always be positive or equal to zero, making the term TΔS always positive or equal to zero. As a result, the value of q must be smaller or equal to TΔS in order for the equation to hold true.

In summary, the reason why q is smaller or equal to T(S2-S1) in the proof of the Helmholtz free energy question is due to the fundamental laws of thermodynamics, specifically the second law which dictates the direction of energy flow in a closed system.
 
  • #4


The Helmholtz free energy is a thermodynamic potential that describes the maximum amount of work that can be extracted from a system at constant temperature and volume. It is defined as F = U - TS, where U is the internal energy of the system, T is the temperature, and S is the entropy.

To answer the question of why q (heat) is smaller or equal to T(S2-S1), we need to understand the relationship between heat, temperature, and entropy. Heat is a form of energy that is transferred from one system to another due to a temperature difference. It is represented by the symbol q. Temperature, on the other hand, is a measure of the average kinetic energy of the particles in a system. Entropy is a measure of the disorder or randomness of a system.

The second law of thermodynamics states that the total entropy of a closed system can never decrease over time. In other words, the entropy of a system can only increase or remain constant. This means that for a reversible process (one that can be reversed without any loss of energy), the change in entropy (S2-S1) is equal to zero. Therefore, q = T(S2-S1) = 0.

For an irreversible process, the change in entropy will be greater than zero, meaning that q < T(S2-S1). This is because some of the heat energy is dissipated as work is done on the system, resulting in an increase in entropy. Therefore, q must be smaller or equal to T(S2-S1) to satisfy the second law of thermodynamics.

In conclusion, the proof of the Helmholtz free energy question shows that q is smaller or equal to T(S2-S1) because of the relationship between heat, temperature, and entropy and the second law of thermodynamics.
 

1. What is Helmholtz free energy?

Helmholtz free energy, also known as Helmholtz energy or A energy, is a thermodynamic potential that measures the amount of work that can be extracted from a thermodynamic system at a constant temperature and volume.

2. How is Helmholtz free energy calculated?

Helmholtz free energy can be calculated using the equation A = U - TS, where A is the Helmholtz energy, U is the internal energy of the system, T is the temperature, and S is the entropy of the system.

3. What is the significance of Helmholtz free energy?

Helmholtz free energy is significant because it provides a measure of the maximum amount of work that can be obtained from a thermodynamic system. It is also used to determine the equilibrium conditions of a system.

4. How does Helmholtz free energy relate to other thermodynamic potentials?

Helmholtz free energy is related to other thermodynamic potentials, such as Gibbs free energy and Enthalpy, through mathematical relationships. These relationships help to determine the equilibrium conditions of a system.

5. In what situations is Helmholtz free energy useful?

Helmholtz free energy is useful in situations where the temperature and volume of a system are constant, such as in closed systems. It is also used in the study of chemical reactions and phase transitions.

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