1. a. You are presented with three identical metal containers of about 5 litres capacity, each about half full of fuel. The containers have a short neck and are normally closed by a screw cap of about 30mm diameter. The cans contain:
(i) petrol (gasoline, flashpoint -43oC),
(ii) methyl alcohol (methanol, flashpoint 11oC), and
(iii) paraffin (kerosine, flashpoint 50oC).
Explain concisely what would happen if the top was taken off and a lit match was immediately dropped into the headspace of each of the cans. Assume that the ambient temperature, and thus that of the liquids, is 15oC. (11 marks)
b. State briefly the relationship between the flash point and auto-ignition temperature of a series of related chemicals, for example methane, propane, butane and pentane. (Completing the table below will help you.) (3 marks)
NAME CHEMICAL FORMULA MOLECULAR WEIGHT FLASH POINT
oC AUTO IGNITION TEMPERATURE oC
According to Wikipedia, "The autoignition temperature or kindling point of a substance is the lowest temperature at which it will spontaneously ignite in a normal atmosphere without an external source of ignition, such as a flame or spark."
Whereas, "The flash point of a flammable liquid is the lowest temperature at which it can form an ignitable mixture in air. At this temperature the vapor may cease to burn when the source of ignition is removed."
Therefore, when we look at the containers given in the question, we can draw the following conclusions regarding what would happen if a lit match was dropped into the space of each can. Based on the definitions above, we are assessing the flash point. Another way to understand flashpoint ...
The solution examines what happens when petrol, methyl alcohol and paraffin is lit with a match in a can. The relationship between flash point and auto ignition temperature is discussed.
Linear Optimization - The Schutzberg Brewery Problem
6. Making Beer. The Schutzberg Brewery has received an order for 1,500 gallons of 3-percent beer (that is, 3 percent alcoholic content). This is a custom order because Schutzberg does not produce a 3-percent product. They do brew the following products.
Product Percent Alcohol Cost per Gallon
Free 0.25 0.55
Light 2.50 0.65
Amber 4.50 0.80
Dark 6.00 0.75
There are 500 gallons of each of these products on hand. Rather than brewing a 3-percent beer from scratch, the brewmaster has decided to mix existing stocks, perhaps with some water (0 percent alcoholic content), to satisfy this small order in the shortest possible time, hoping that the taste will be adequate. In case the taste is bad and he has to throw the mixture out, he would like to minimize the cost of the mix.
a. What are the components of the least-cost blend that will result in a 3-percent beer?
b. What is the total cost for the 100 gallons of product?
c. Use the pattern in (b) to trace the effects of increasing the requirement by 10 percent. How will the optimal mix change? How will the optimal cost change?