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 16.0-L 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 β = 400×10 – 6 / ºC ? Note that this coefficient is approximate, because most car radiators have operating temperatures of greater than 95.0ºC.
= [(400x10-6 /oC - 51 x 10-6 /oC) (16L) (95oC - 10oC)]
= [(349 x 10-6 /oC) ( 16L) (85oC)]
= 0.475 L
The change in volume is 0.475 L