# On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field

## Abstract

**:**

## 1. Introduction

#### 1.1. Problem Statement: The Heating of Two Spheres in a Gravitational Field

^{−1}[3,4]. For normal gravity, then $R<6.9\times {10}^{6}$ m. So as long as the copper sphere is smaller than the Earth, this condition will be satisfied!).

#### 1.2. Cyclic Process Based on the Heating of a Sphere in a Gravitational Field

## 2. Thermodynamically Consistent Analysis

#### 2.1. What If the Sphere Is Surrounded by the Atmosphere?

#### 2.2. What If There Is No Atmosphere Surrounding the Sphere?

## 3. Equivalent Cyclic Process for an Ideal Gas in a Container in a Gravitational Field

#### 3.1. Ignoring the Effects of Gravity on the Properties of the Ideal Gas

#### 3.2. Including the Effects of Gravity on the Properties of the Ideal Gas

## 4. Evaluation of the Entropy Changes of the Ideal Gas Around the Cycle

## 5. Conclusions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Sphere A rests on a horizontal platform, while sphere B is suspended from a thread that is attached to another horizontal platform that is at a higher height in the gravitational field with strength $g$ (and pointing in the downward direction). Both spheres expand upon an increase in their temperatures, such that the center of mass of sphere A is raised, while that of B is lowered in the gravitational field.

**Figure 2.**An ideal gas is contained within a cylinder of a constant cross-sectional area with a movable piston of negligible mass. In the first step 1 of this reversible cyclic process, and while the cylinder remains on the lower platform, the temperature of the ideal gas is increased from ${T}_{1}$ to ${T}_{2}$. The pressure on the piston remains at ${P}^{*}$ while the height of the piston also increases from ${h}_{1}$ to ${h}_{2}$. In the second step 2, the piston is held in placed by a rigid connecting rod attached to the upper platform. While keeping the pressure on the piston again at ${P}^{*}$, the temperature of the gas is decreased from ${T}_{2}$ to ${T}_{1}$, while the relative height of the piston from the bottom of the cylinder is decreased from ${h}_{2}$ to ${h}_{1}$. Consequently, the center of mass of the gas has been raised in the gravitational field. In the final step 3, the cylinder is returned to the lower platform without changing the temperature and volume of the gas. Hence, the center of mass of the gas has been returned to its initial height, as it was at the beginning of the cycle and prior to the start of step 1.

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Corti, D.S.
On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field. *Symmetry* **2019**, *11*, 930.
https://doi.org/10.3390/sym11070930

**AMA Style**

Corti DS.
On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field. *Symmetry*. 2019; 11(7):930.
https://doi.org/10.3390/sym11070930

**Chicago/Turabian Style**

Corti, David S.
2019. "On the Assumption of the Independence of Thermodynamic Properties on the Gravitational Field" *Symmetry* 11, no. 7: 930.
https://doi.org/10.3390/sym11070930