Final answer:
The water in an automobile radiator will expand when heated, potentially leading to overflow. Calculating the change in volume with the given volume coefficient of expansion shows that 0.544 liters of radiator fluid will overflow when the temperature reaches 95.0°C. A coolant reservoir typically catches this excess fluid to prevent damage and maintain proper coolant levels.
Step-by-step explanation:
When an automobile radiator is filled to the brim with water and the engine is running, causing the water temperature to rise, the water will expand due to an increase in temperature. This phenomenon can be analyzed using the water's volume coefficient of expansion. In the case of a radiator filled to a 16.0-L capacity at 10.0°C, we want to calculate the volume that will overflow when the temperature reaches 95.0°C, given that the fluid's volume coefficient of expansion is 400×10-6/°C.
To calculate the change in volume, we use the formula: ∆V = β V0 ∆T, where ∆V is the change in volume, β is the volume coefficient of expansion, V0 is the original volume and ∆T is the change in temperature. Substituting the known values, we get ∆V = (400×10-6/°C) x 16.0 L x (95.0°C - 10.0°C). Therefore, ∆V = 0.544 L, which means that 0.544 liters of radiator fluid will overflow from the radiator at 95.0°C.
It's important to note that the overflow occurs because the expansion of water is far greater than the expansion of the radiator material, usually copper or another metal, and that is why most automobiles include a coolant reservoir to catch any excess fluid. This design prevents damage to the engine and maintains the appropriate amount of coolant within the system.