How does temperature affect vapor pressure?

• Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid.
• As temperature increases, vapor pressure usually increases.

The Pressure dataset contains 19 observations of mercury vapor pressure at different temperatures.

• Temperature: degrees Celsius
• Pressure: mm Hg

##   temperature pressure
## 1           0   0.0002
## 2          20   0.0012
## 3          40   0.0060
## 4          60   0.0300
## 5          80   0.0900
## 6         100   0.2700

The sample mean is calculated using:

\[ \bar{x} = \frac{1}{n}\sum_{i=1}^{n}x_i \]

With the sample mean, we can calculate the average vapor pressure.

Mean pressure: 124.34 mm Hg

Median pressure: 8.8 mm Hg

The difference between these values shows that the pressure data is skewed toward higher values.

Vapor pressure increases rapidly at higher temperatures.

The code generates the previous plot:

ggplot(pressure, aes(x=temperature, y=pressure)) +
  geom_point() +
  geom_line() +
  labs(
    x = "Temperature (°C)",
    y = "Vapor Pressure (mm Hg)"
  ) + theme_minimal()

Since vapor pressure increases rapidly, we can use a logarithmic scale to make smaller values easier to compare.

The transformation is:

\[ P_{\text{Log}} = log_{10}(P) \]

Where:

• \(P\) = Original vapor pressure
• \(P_{\text{Log}}\) = Log-transformed pressure

A logarithmic scale helps visualize measurements spanning a large range.

The logarithmic scale makes the changes at lower pressures easier for us to see.

Hover over the points to see their temperature and pressure values.

Based on visualizing the data, we’ve learned that:

• Vapor pressure increases as temperature rises.
• The relationship is nonlinear.
• Logarithmic scales help visualize large ranges of values.