Question

Most automobiles 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 16.0L capacity when at 10.0ºC. What volume of radiator fluid will overflow when the radiator and fluid reach their 95.0ºC operating temperature, given that the fluid’s volume coefficient of expansion is (beta=400times10^6/ºC)?

A) (0.43 L)
B) (0.86 L)
C) (1.29 L)
D) (1.72 L)

Answer 1

Approximately 0.54 L of radiator fluid will overflow when the radiator and fluid reach their 95.0°C operating temperature.

Step-by-step explanation:

The volume of radiator fluid that will overflow can be calculated using the formula:

∆V = Vβ∆T

∆V = change in volume

V = initial volume

∆T = change in temperature

β = volume coefficient of expansion

Given that the initial volume is 16.0 L, the volume coefficient of expansion is 400×10-6/°C, and the change in temperature is 85.0°C (95.0°C - 10.0°C), we can calculate the volume of radiator fluid that will overflow:

∆V = 16.0 L × 400×10-6/°C × 85.0°C = 0.544 L

Therefore, approximately 0.54 L of radiator fluid will overflow when the radiator and fluid reach their 95.0°C operating temperature.