A sealed can is filled completely with methyl alcohol. Which of these materials could the can be made of so that it would not rupture when the whole system was cooled by 20 degrees Celsius?
A.)Aluminum
B.)Fused quartz
C.)Copper
D.)Any of these
E.)None of these
To answer this question, we need to consider the coefficient of thermal expansion of each material and its effect on the can when it is cooled by 20 degrees Celsius.
The coefficient of thermal expansion (CTE) measures how much a material expands or contracts when the temperature changes. A higher CTE means a material expands or contracts more with temperature changes.
In this case, we want the can to be made of a material with a low CTE so that it does not expand or contract significantly when cooled by 20 degrees Celsius. This will prevent any potential rupture of the can.
Let's analyze each material:
A) Aluminum: Aluminum has a relatively high CTE, which means it expands and contracts quite a bit with temperature changes. Therefore, it is unlikely that the can made of aluminum would not rupture when cooled by 20 degrees Celsius.
B) Fused quartz: Fused quartz has an extremely low CTE, which means it expands and contracts very minimally with temperature changes. Therefore, the can made of fused quartz is a possible option that would not rupture when cooled by 20 degrees Celsius.
C) Copper: Copper has a moderate CTE. Although it expands and contracts less than aluminum, it still has a relatively high CTE. Therefore, it is unlikely that the can made of copper would not rupture when cooled by 20 degrees Celsius.
D) Any of these: Since we have determined that fused quartz is a suitable material, but the other options (aluminum and copper) may not be, we can conclude that "Any of these" is not the correct answer. It implies that all the options are suitable, which is not the case.
E) None of these: This is the most likely correct answer. As we have discussed, fused quartz is the most suitable material due to its extremely low CTE. Aluminum and copper are less suitable due to their higher CTE values.
In conclusion, the can should ideally be made of fused quartz (option B) to ensure that it does not rupture when cooled by 20 degrees Celsius. So, the correct answer is B.) Fused quartz.