Feedback from the previous e-zine (see website) prompted me to issue this “unscheduled” interruption of my train ride from New York to Washington. First, Las Vegas is still in Nevada (not Arizona). When my example of a city in a hot climate changed from Phoenix (AZ) to the better-known Las Vegas (NV), I neglected to change the state. My apologies for the oversight.
More importantly, the previous e-zine discussed the use of volumetric units (such as gallons) to infer mass when the composition and temperature is known. The example given was that of purchasing a gallon of gasoline in a hot and cold climate. The assertion was that a gallon of gasoline purchased in hot and cold climates might have different sizes due to their differing temperatures, but their masses should be the same because the retail flowmeter is temperature compensated.
A number of e-mails questioning this assertion and further investigation resulted in the interesting discovery that retail gasoline flowmeters are not temperature-compensated in the United States, but are temperature-compensated in Canada. In other words, either the measured volume (in the US) or the measured temperature-corrected volume (in Canada) is used to infer mass.
Consider the following general analysis:
- Air temperature differences between hot and cold climates are large. In addition, air temperature fluctuations between day and night in a given location can be large.
- There is a significant difference between ground temperatures in hot and cold climates. However, ground temperature fluctuations between day and night in a given location is very small. Ground temperature fluctuation between summer and winter in a given location is relatively small.
- Gasoline will be warm when it leaves the refinery, but will cool in transport to the retailer’s underground tank. Given time in the tank, the temperature of the gasoline will approach the ground temperature.
- Flowmeter calibration is performed using standard weights, implying a calibration to mass.
These statements imply that despite wide air temperature fluctuations, the temperature of the gasoline pumped through the flowmeter should be nearly the same as the ground temperature. Because the ground temperature does not fluctuate very much, the temperature variation of the gasoline will be small throughout the year, so the mass of a gallon of gasoline should not vary much throughout the year from a given tank. Following this logic, the mass of a gallon of gasoline sold in Alaska should be the same as one sold in Nevada.
Fluctuations in gasoline temperature cause gasoline density changes. The magnitude with which these changes affect measurement accuracy can be quantified by performing an uncertainty analysis to determine if temperature compensation is appropriate. An uncertainty analysis for this measurement would likely reveal a number of sources of measurement uncertainty, such as (but not limited to) the effects of ambient air temperature, gasoline temperature leaving the refinery, transport time from the refinery to the tank, ground temperature, tank level prior to filling, the volume of gasoline in the flowmeter piping, flowmeter piping temperature, frequency of use, and composition changes. As a minimum, such analysis would likely reveal that the consumer would not be advised to purchase gasoline from a tank that was just filled with warm gasoline. A detailed analysis may reveal other significant issues.
While this is perhaps more information than one would like to know about the subject, this discussion clearly illustrates the need to understand the process — and that the same process may be different in different locations. Sometimes… it’s just not so easy.