1. A factory disposes its waste into a nearby stream at the rate of 10,000 gallons per hour. Plant regulations state that this waste cannot exceed 80°C in temperature when entering the water. A plant supervisor wants to test this temperature but cannot do it directly since the pipeline enters below ground. He does however determine the temperature of the stream above the waste entry to be 25°C and the temperature below the pipeline to be 27°C. If the volume flow of the stream is calculated to be 250,000 gallons, what is the temperature of the waste? Does it meet industry standards?
2. How much 15°C water is needed to cool down 200 milliliters of 65°C coffee to 60°C? What physical constraints might exist which are not reflected in the mathematical solution of this problem?
3. Suppose you are working in a situation where the volumes and TH are all known. Rewrite your formula so that TM is represented as a function of TC. What kind of function is this? What does VC/VM represent? What does VHTH/VM represent?
4a. Now suppose that instead of mixing two volumes of different temperatures, you are instead mixing two volumes of different acidity percentiles. Adapt your previous formula to solve the following: If 40 milliliters of 35% acidic solution is mixed with 50 milliliters of 60% acidic solution, what is the acidity level of the resulting mix?
4b. Describe the experimental procedure you would need to complete to test the validity of your new formula. Does it work with varying volumes and percentiles?