Thermodynamic Entropy question

In summary, the Gibbs free energy of benzene decreases with increasing temperature while at a constant pressure, exhibiting three linear segments corresponding to the solid, liquid, and gas phases. The slopes of these segments increase in magnitude as the phase changes from solid to liquid, and liquid to gas. Using the formula (dG/dT)_P = −S, it can be shown that the entropy of the gas phase is greater than that of the liquid and solid phases. This is evident by drawing tangent lines in each region and observing the positive or negative slope and comparing the magnitudes of these slopes.
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subtletuna
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Homework Statement



The Gibbs free energy of benzene decreases continuously with temperature (at fixed pressure) and shows three nearly linear segments corresponding to the solid, liquid and gas phases. The magnitude of the slopes increases as one moves from solid to liquid, and liquid to gas.
Use the formula (dG/dT)P = −S to show that S(gas) > S(liquid) > S(solid).

Homework Equations



(dG/dT)_P = −S

The Attempt at a Solution


I have no idea where to begin sadly =\... I made a graph of G vs T, but i don't think that helps much.
 
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Draw tangent lines in the solid, liquid, and gas regions. Are the slopes positive or negative, and how do the magnitudes compare?
 

1. What is thermodynamic entropy?

Thermodynamic entropy is a measure of the disorder or randomness in a system. It is a fundamental concept in thermodynamics and is closely related to the second law of thermodynamics.

2. How is thermodynamic entropy calculated?

Thermodynamic entropy is typically calculated using the Boltzmann equation, which takes into account the number of possible microstates (or arrangements) of a system. It is also related to the change in heat and temperature of a system.

3. What is the relationship between thermodynamic entropy and energy?

Thermodynamic entropy and energy are closely related, but they are not the same thing. Entropy is a measure of the energy dispersal or randomness in a system, while energy is a measure of the ability of a system to do work or cause change.

4. Can thermodynamic entropy be decreased?

In a closed system, thermodynamic entropy will always increase or stay the same. This is a fundamental principle of the second law of thermodynamics. However, it is possible to decrease the local entropy in a system by increasing the entropy in the surrounding environment.

5. What are some real-life examples of thermodynamic entropy?

A common example of thermodynamic entropy is the dispersal of energy in the form of heat. When a hot object is placed in a cold environment, the energy will disperse and the system will reach thermal equilibrium, resulting in an increase in entropy. Other examples include the mixing of liquids and gases, and the decay of radioactive materials.

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