Water boiling point according to daily pressure
2023-09-25
Defining boiling point
The boiling point of a substance is the temperature at which the vapor pressure of that substance is equal to atmospheric pressure. This relationship can be described with the Clausius-Clapeyron Equation.
\(ln(\frac{P_1}{P_2}) = \frac{\Delta H_{vap}}{R}(\frac{1}{T_2}-\frac{1}{T_1})\)
The enthalpy of vaporization of water \(\Delta H_{vap} = 40.7 \frac{kJ}{mol}\) and the gas constant \(R = 8.3145 \frac{J}{mol K}\)
The vapor pressure of water is 1.0 atm at 373 K. We can use this known relationship to calculate the daily boiling point of water with the Clausius-Clapeyron Equation. NCAR records atmospheric pressure at the Foothills Laboratory in Boulder, Colorado in units of hectopascals 1.0 atm = 1,013.25 hPa.
Extracting pressure data
2023 Weather data were extracted for this analysis from the foothills laboratory (ftp://ftp.eol.ucar.edu/pub/archive/weather/foothills). Data were processed for atmospheric pressure, recorded every five minutes.
file_names <- list.files(path = "weather_data/")
pressure_data <- lapply(paste0("weather_data/", file_names), function(i){
date <- unlist(str_split(i, "\\."))[2]
nc_data <- nc_open(i)
t <- ncvar_get(nc_data, "time")
pressure <- ncvar_get(nc_data,"pres")
tibble(date = as_date(date),
time_sec = t,
pressure_hPa = pressure)}) %>%
reduce(full_join, by = c("date","time_sec","pressure_hPa")) %>%
mutate(date = date + seconds(time_sec)) %>%
select(-time_sec)
ggplot(data=pressure_data,aes(x=date,y=pressure_hPa)) +
geom_line() + theme_classic() + labs(y = 'Boiling Point (°F)', x = 'Date')
Calculating boiling point according to atmospheric pressure
To calculate the boiling point over time in Boulder, the Clausius-Clapeyron equation can be rearranged to
\(T_2 = \frac{1}{\frac{R}{\Delta H_{vap}} (\frac{P_1}{P_2}) + \frac{1}{T_1}}\)
By applying this equation to the NCAR dataset, we can determine the variation in the boiling point of water across 2023 (up to September).
clausius_func_water <- function(pressure){
R <- 8.3145/1000
# Divide by 1000 to convert gas constant from J to kJ
delta_H <- 40.7
1/((R/delta_H)*log(1013.25/pressure) + (1/373))
}
pressure_data <- pressure_data %>%
mutate(date = date(date)) %>%
group_by(date) %>%
summarise(pressure_hPa = mean(pressure_hPa)) %>%
# Calculate daily mean pressure from five minute increments
mutate(boiling_point_K = clausius_func_water(pressure_hPa)) %>%
mutate(boiling_point_F = (boiling_point_K - 273.15) * 1.8 + 32)
line_plot <- ggplot(data=pressure_data,aes(x=date,y=boiling_point_F)) +
geom_line() + theme_classic() + ylab('Boiling Point (°F)')
boxplot <- ggplot(data=pressure_data,aes(y=boiling_point_F)) +
geom_boxplot() + scale_x_discrete() + theme_classic() +
ylab('Boiling Point (°F)')
plot_grid(line_plot,boxplot, rel_widths=c(2,1))
mean <- mean(pressure_data$boiling_point_F)
range <- max(pressure_data$boiling_point_F) - min(pressure_data$boiling_point_F)