Final answer:
By using the formula for thermal expansion, it is calculated that approximately 0.544 liters of antifreeze will overflow from the car radiator when its temperature increases from 10.0°C to 95.0°C.
Step-by-step explanation:
Calculating Overflow Volume from a Car Radiator
To determine the volume of radiator fluid that will overflow when the radiator and the fluid reach a given operating temperature, we need to apply the concept of thermal expansion. The volume expansion can be calculated using the formula ΔV = βV₀ΔT, where β is the volume coefficient of expansion, V₀ is the initial volume and ΔT is the change in temperature.
In this case, a car's radiator is filled to its 16.0-L capacity at 10.0°C, and we need to find out the overflow volume when it reaches 95.0°C. Given β (the coefficient of expansion) is 400×10-6/°C, we can find the change in volume as follows:
ΔV = βV₀ΔT
= (400×10-6/°C)(16.0 L)(95.0°C - 10.0°C)
= (400×10-6)(16.0)(85.0)
= 0.544 L
Therefore, the volume of antifreeze that will overflow is approximately 0.544 liters.