Chemical and mechanical engineers often need to know the vapour pressure of water for specific temperatures....

   

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Chemical and mechanical engineers often need to know the vapour pressure of water for specific temperatures. Physical chemistry suggests that the vapour pressure should follow an exponential relationship to the inverse of the temperature. Specifically, let p, be the vapour pressure and T be the temperature, the Clausius-Clapeyron equation states that In p, is directly proportional to -1/T, that is 1 In p, ox T The following table lists the vapour pressures of water for various temperature (in Kelvin) from 0°C to 100°C. Temperature (K) Vapor pressure (mm Hg) 273 4.6 283 9.2 293 17.5 303 31.8 313 55.3 323 92.5 333 149.4 343 233.7 353 355.1 363 525.8 373 760.0 (a) Produce a scatter plot of the data. (b) Let y; be the natural log of the ith vapour pressure and let r, be the inverse of the ith temperature. The Clausius-Clapeyron equation suggests that a reasonable model for the vapour pressures over a wide range of temperatures is Yi = Bo + B1x; +6. Produce a scatter plot of the transformed data. Fit the regression model to the data and plot this regression line on the same graph with the transformed data. (c) Convert the prediction equation back to the original metric and plot this curve on the same graph with the original data. Chemical and mechanical engineers often need to know the vapour pressure of water for specific temperatures. Physical chemistry suggests that the vapour pressure should follow an exponential relationship to the inverse of the temperature. Specifically, let p, be the vapour pressure and T be the temperature, the Clausius-Clapeyron equation states that In p, is directly proportional to -1/T, that is 1 In p, ox T The following table lists the vapour pressures of water for various temperature (in Kelvin) from 0°C to 100°C. Temperature (K) Vapor pressure (mm Hg) 273 4.6 283 9.2 293 17.5 303 31.8 313 55.3 323 92.5 333 149.4 343 233.7 353 355.1 363 525.8 373 760.0 (a) Produce a scatter plot of the data. (b) Let y; be the natural log of the ith vapour pressure and let r, be the inverse of the ith temperature. The Clausius-Clapeyron equation suggests that a reasonable model for the vapour pressures over a wide range of temperatures is Yi = Bo + B1x; +6. Produce a scatter plot of the transformed data. Fit the regression model to the data and plot this regression line on the same graph with the transformed data. (c) Convert the prediction equation back to the original metric and plot this curve on the same graph with the original data.