Question

Most cars have a coolant reservoir to catch radiator fluid that may overflow when the engine is hot. A radiator is made of copper and is filled to its 16.0-L capacity when at 10.0°C. What volume of radiator fluid will overflow when the radiator and fluid reach a temperature of 95.0°C, given that the fluid’s volume coefficient of expansion is β=400×10⁻⁶/°C? (Your answer will be a conservative estimate, as most car radiators have operating temperatures greater than 95.0°C).

(a) 0.23 L
(b) 0.31 L
(c) 0.42 L
(d) 0.54 L

Answer 1

The volume of radiator fluid that will overflow at 95.0°C is calculated using the fluid's volume coefficient of expansion, the initial volume, and the temperature change. The result is an overflow volume of 0.54 L. Therefore, the correct answer is (d) 0.54 L.

Step-by-step explanation:

To find out the volume of radiator fluid that will overflow when the radiator and fluid reach 95.0°C, we first calculate the expansion of the fluid using the volume coefficient of expansion (β) and the change in temperature (ΔT).

The initial volume (V0) of the radiator fluid is 16.0 L, the volume coefficient of expansion (β) is given as 400×10-6°C-1, and the temperature change (ΔT) is from 10.0°C to 95.0°C, so ΔT = 95.0°C - 10.0°C = 85.0°C.

The change in volume (ΔV) is given by the formula ΔV = β × V0 × ΔT. Plugging in the values:

ΔV = 400×10-6°C-1 × 16.0 L × 85.0°C

ΔV = 0.544 L

This volume is the amount that the radiator fluid has expanded by. Since the radiator cannot hold this additional volume, this amount of fluid will overflow. The correct answer to the question is that 0.54 L of radiator fluid will overflow.