The Sky's the Limit with the Clapeyron-Clausius Equation

Chapter Listing

Home: Journey to the Clapeyron-Clausius Equation

Chapter One: The Gibbs Equation

Chapter Two: The Tds Equation

Chapter Three: The Maxwell Relations

Chapter Four: The Clapeyron Equation

Chapter Five: The Clapeyron-Clausius Equation

Experiment: Complete the Journey From Home: Fun Experiment!

Real World Applications: The Sky's the Limit with the Clapeyron-Clausius Equation

References: References

Now that you've completed the perilous journey to the Clapeyron-Clausius equation and taken the quiz, you may be wondering why you bothered in the first place. Passing your exam should be incentive enough. However, throughout your career you will have plenty of opportunities use your newfound skills.

One such field is meteorology, more specifically the study of condensation in the atmosphere. Also known as,

Clouds

The Clapeyron-Clausius equation forms the basis of meteorology and our understanding of clouds. Why? Clouds are water vapor that has become risen into the atmosphere, reached a certain temperature and pressure, and condensed. The Clapeyron-Clausius equation is almost perfect for analyzing this scenario! The equation itself can be written expressing saturation pressure as a function of temperature. [3]

Where C is an integration constant. However, because the latent heat of water varies with temperature, this formula is only an estimation. Thankfully, the August-Roche-Magnus equation serves as a better approximation.[3]

Where T is in °C and P is in hPa (1hPa = 100Pa). This is extremely useful because it expresses the saturation pressure as a function of temperature. Obviously, this is still a very rudimentary equation and cannot be used to accurately predict complex cloud patterns. However, it does reveal a fundamental relationship between saturation pressure and temperature of water vapour. For example, if the pressure of a specific region in the atmosphere were to be known, the predicted temperature of the region could be used to predict rainfall or vice versa.

Climate Change

The Clapeyron-Clausius equation has also been used in developing predictions in changes to our climate. Using the Clapeyron-Clausius equation and it's further derivations such as the August-Roche-Magnus equation, it is possible to estimate the percentage increase in water vapour present in the atmosphere. Using the Clapeyron-Clausius scaling prediction the fractional rate of change in water vapour in our atmosphere was found to be around 7%[1]. This represents a serious problem, as water vapour itself is a greenhouse gas that will further contribute to global warming. It also results in hotter and more humid conditions throughout the globe. This could result in a worldwide increase in insects that prefer hot and damp climates such as mosquitoes.

Through the use of the Clapeyron-Clausius equation scientists can predict the various effects of climate change on the earth. With this information, humanity can better prepare for the inevitable changes to our earth. The severity of these predictions may hopefully help to persuade humanity to make some essential changes to the way we live and how society functions.

Space Exploration

The Journey to the Clapeyron-Clausius Equation is not limited to the confines of earth. It is a journey that takes us to space, the final frontier.

Just as the Clapeyron-Clausius equation can be used by meteorologists on earth to help predict weather patterns, it can also be used to help analyse the atmospheres of other planets. Most planets have their own complex and unique atmospheres. The composition and behaviours of which can reveal many interesting properties of the planets themselves. The Clapeyron-Clausius equation can be used to aid in this analysis.

The Clapeyron-Clausius equation can be used to model the density, pressure, and height of the clouds of various different planets, despite their varying compositions.[2] So long as the compositions of the clouds are known, as well as the latent heat of vapourisation and the specific gas constant, the formula may still be applied.

To Conclude

Well, perhaps not entirely. However, the Clapeyron-Clausius equation does form a building block that more complicated and accurate models are based upon. The Clapeyron-Clausius equation can be used in a multitude of ways and engineers are still finding uses for it in the most unexpected of fields. An understanding of the Clapeyron-Clausius equation and it's implications is vital to success in all of these three fields and more. We hope that your journey has taught you many things about the Clapeyron-Clausius equation and a little about thermodynamics in general. The truth is, the Journey to the Clapeyron-Clausius equation is just the beginning. I wish you well on your future journeys, may they be a little more exciting than this one.