# How to apply the Clausius-Clapeyron to geysers

• Elemere
In summary, the conversation is about someone's involvement in a physics competition and their struggle to determine the heat of the water at the bottom of a geyser using the Clausius-Clapeyron relation. They have found a helpful YouTube video but are still having trouble getting the correct result. The conversation includes values given and a link to the video.
Elemere
Hi first post so forgive any break in widely accepted conduct,
Currently involved in a physics competition one of the question is to investigate geysers. Time and time again I have stumbled upon reference to Clausius-Clapeyron relation. Probably the best source I have come across is a youtube video and while able to replicate his results of total pressure by using his variables I am still unable to determine the heat of the water at the bottom of the geyser. Below I will paste the youtube video and my math that isn't working.

Arrangement of relation given:
http://file:///C:/Users/ryan/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png

Values given:
P1 = aprox 100000 (atmospheric pressure)
P2 = 113000
Delta Hvap = 2.6*10^6 (latent heat of vaporization H2O)
R = 8.314 (gas constant)
T2 = ?
T1 = 100C (boiling point I assume)

When these values are input into the relation the result is 100.0045 when the video states it should be 103 inputting other values doesn't seem to move T2 far from 100.Youtube vid:

Last edited by a moderator:
I am so sorry and if someone would tell me how I could take this down I would appreciate it. I assumed Hvap was latent heat of vaporization when really it is change in enthalpy which has a value of 41000 J/mol.

## 1. How does the Clausius-Clapeyron equation apply to geysers?

The Clausius-Clapeyron equation is a thermodynamic relationship that can be used to predict changes in the boiling point of a substance with changes in pressure and temperature. In the case of geysers, the equation can be used to explain why the water inside the geyser reaches boiling point and erupts into a hot spring.

## 2. What are the key variables in the Clausius-Clapeyron equation?

The key variables in the Clausius-Clapeyron equation are temperature, pressure, and the heat of vaporization of the substance. These variables are all related and can be used to calculate the change in boiling point of a substance with changes in pressure and temperature.

## 3. How does the boiling point of water change with increasing elevation?

According to the Clausius-Clapeyron equation, as pressure decreases with increasing elevation, the boiling point of water also decreases. This is why water boils at a lower temperature at higher altitudes, such as in the case of geysers located in mountainous regions.

## 4. Can the Clausius-Clapeyron equation be used to predict eruptions of geysers?

While the equation can provide insight into the thermodynamic processes involved in geyser eruptions, it is not accurate enough to predict specific eruption times. This is because there are many other factors, such as the shape and size of the geyser's vent, that also play a role in determining eruption times.

## 5. How is the Clausius-Clapeyron equation applied in the study of geysers?

The Clausius-Clapeyron equation is used in the study of geysers to better understand the thermodynamic processes that occur within them. By analyzing changes in pressure and temperature, scientists can gain insights into the mechanisms that drive geyser eruptions and make predictions about their behavior.

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