One day, Brother Gregory and Brother Matthew had an argument. They were sitting in Brother Victor's kitchen and were about to eat a bowl of soup.
"This is too hot!" shouted Brother Matthew, throwing down his spoon. "I have a sensitive mouth, and my tongue tells me that Brother Victor has overheated this broth.
"No he hasn't," retorted Brother Gregory, who likes his crab-leg soup at much higher temperatures. "There is just the right amount of heat in this dish. It has been heated to perfection!"
"It's a pity you broke the thermometer this morning," Brother Matthew replied, "or we could have taken the temperature of the soup and you would have seen I was right."
"You are never right," Brother Gregory told him, "and anyway, I didn't break the thermometer, you sat on it!"
"Let's not argue," Brother Matthew hurried on, turning red, "how are we going to take the temperature of this soup if we don't have a calibrated thermometer?"
"I know," his friend said, with a slight smile, "I'll ask my research assistant to make more thermometers and test them. Then we will use one of these new thermometers to take the temperature of the soup. That is when we will see that I am right!"
So they agreed to ask you to help them make and test four new thermometers. Brother Gregory has given you four different liquids; a ruby liquid -:- a gold liquid -:- an emerald liquid -:- and an azure liquid .
Each of these liquids expands and takes up more volume in response to higher and higher temperatures. If they are placed in a thin glass tube they will increase in volume and fill more of the tube as the temperature increases. In this way it is possible to make a "temperature measuring device" (a thermometer) which can be calibrated and then used to measure the average kinetic energy in any substance (its temperature).
Brother Gregory wants you to use thermometers containing these four liquids and find out how they respond to different amounts of heat in water.
Tools of the Trade
Each of the thermometers has been made by trapping a small amount of the experimental liquid in a bubble at the end of a long thin glass tube. The "bubble" of liquid is a reservoir with very thin walls through which the heat can pass quickly and easily. As the liquid expands it pushes up the thin, empty tube and the amount it has expanded can be read on an arbitrary scale etched onto the side of the glass tube.
This is the classic way of making a thermometer. But before it can be used to measure the temperature of an unknown liquid (the soup), it is necessary to calibrate the experimental thermometer by placing it in known amounts of "heat".
You must place each type of thermometer into a known amount of water containing a known number of calories of energy. You must then measure how much the liquid expands. Each liquid will behave differently.
Making the Calculation
Temperature is simply a measure of the average kinetic energy of an individual molecule. In this investigation you must first calculate the number of calories per gram in the water surrounding the thermometer.
calories/gram = number of calories / amount of water (grams)
Cg = C / W
Where Cg is the calories per gram value, W is the amount of water used, and C is the number of calories put into the water.
The thermometer can now be calibrated by finding out how far the liquid expands up the tube for each unit of Cg value.
If E is the expansion value, and D is the distance that the liquid has moved up the tube, then
E = D / Cg
Each liquid will have a different expansion value (E value). You must find out the E value for each of the four liquids.