## Problems 3

### Understanding the Past & Present, Predicting the Future

Scientists try to understand the world.  Scientists determine if their understanding is valid by making PREDICTIONS then checking if those predictions are correct.  Precise mathematical quantities are considered better predictions than vague word descriptions.  Science can't actually PROVE their understanding is TRUE.  The best scientists can do is to check predictions.  So solving problems and making predictions are essential to establish the VALIDITY of the scientific theories.  This checking against reality is the part of science that distinguishes it from philosophy.  Beyond just being a part of science, checking the predictions is the very aspect of science that makes science so valuable to civilization.  Without solving problems (i.e., making and checking predictions) you really haven't learned the skills of science.

The following problems are intended to focus your thinking, help you understand our world, and to make predictions that are verifiable.  Keep your thoughts and predictions for these problems in your journal.  Include sufficient information so you can later refer back to your journal to refresh your thoughts and memories.

1. Adjectives are used to describe objects.  Some adjectives describe properties that are characteristic of the material substance from which the object is made while others describe features of that particular object.  It is worth distinguishing.  Decide which of the following adjectives describes properties of the substance and which describe the particular object:
1. A sharp, heavy, shiny, stainless-steel knife.
2. A 5.0 g chunk of black tar.
3. A beautifully carved wooden chair.

2. Sketch what a graph would probably look like if you measured some super-heated steam at 300°C cooling, condensing to liquid at 100°C, and continuing to cool to room temperature.

3. What does it mean when a temperature verses time graph has a level plateau?

4. What was happening if a line on a temperature verses time graph drops steeply to the right?

5. Consider a parking lot with many cars:
1. Does the number of wheels in the lot depend on the number of cars?
2. Does the number of wheels per automobile depend upon the number of cars?
3. Is the number of wheels in the parking lot a characteristic property?
4. Is the number of wheels per car a characteristic property?
5. Draw a sketch of a graph of the number of wheels in a parking lot as a function of the number of cars.
6. Draw a sketch of a graph of the number of wheels per car as a function of the number of cars in the lot.

6. Do the following calculations expressing the answers to the correct number of digits.
1. 125 / 23.7
2. 20.5 / 51.0
3. 0.065 / 32.5
4. 123 / .72

7. A 10.0 cm3 block of silver (metal) has a mass of 105 g.  What is the density of silver?

8. A 5.0 cm3 block of rock salt (= table salt) has a mass of 10.7 g.  What is the density of rock salt?

9. A 0.50 cm3 sample of alcohol has a mass of 0.41 g.  What is the density of the alcohol?

10. Suppose you receive two clear, colorless liquids.  You measure their volumes and masses.
1. What would you conclude if you calculated their densities to be 0.98 g / cm3 and 0.78 g / cm3?
2. What would you conclude if you calculated their densities to be 0.81 g / cm3 and 0.79 g / cm3?

11. A hydrometer is a device designed to float in a liquid, revealing the density of the liquid by how high or low the hydrometer floats.  Like a thermometer, a narrow neck on the hydrometer is used to amplify the differences.  Hydrometers are used to measure differences in the density of the sulfuric acid in car batteries.  As a battery is discharged, the H2SO4 in the acid reacts with the lead metal plates leaving the acid less dense.  Hydrometers are also used to check the composition of antifreeze in car radiators.  The density of the cooling water is greater when it contains more antifreeze.  Hydrometers are also used to monitor the fermentation process creating wine and hard cider.  Ethyl alcohol is less dense than water so the density decreases as the concentration of alcohol increases.  Read the density from the hydrometer shown here.

12. A mixture of 1.0 g of baking soda is combined with 8.8 g of sulfuric acid in a container connected by a flexible tube to an apparatus for collecting gas by displacement of water.  200 cm3 of gas was collected.  The remaining acid and solid have a mass of 9.4 g.  What is the density of the gas produced?

13. If the gas collected in the above experiment is compressed to 50 cm3, what will be the new density of the gas?

14. Carbon dioxide collected in Experiment 3-6 dissolves slightly in water.  How does this effect the volume of gas you collected?  How does this effect your calculation of the density of carbon dioxide?

15. A small container contains 50 cm3 of liquid.
1. If the liquid is methyl alcohol with a density of 0.79 g / cm3, what will be its mass?
2. If the liquid is water with a density of 1.0 g / cm3, what will be its mass?

16. Estimate the mass of air in the room where you are at given that the density of air is about 1.2 x 10-3 g / cm3.

17. Ice is placed in Styrofoam coolers in the Summer to keep contents cold.  How would adding more ice effect the temperature of the contents?  What would be the value of having more ice in the cooler?

18. A double boiler is a set of kitchen pots with water boiled in the bottom pot and food cooked in a top second pot, warmed by the steam.  Food cooked directly on the burner can approach the temperature of the heat source.  How hot can the food in a double boiler get?

19. How could use density to distinguish between unlabelled containers of milk and cream?

20. How does the density of air change if it is heated?  How is this used in hot air balloons?

If you need credit for this study, use complete sentences so that your thoughts and predictions are not just unintelligible words and numbers, but make sense to whomever is the reader.

created 11/28/2003
revised 11/29/2003
by D Trapp