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 16.0-L capacity when at 10.0∘C. What volume of radiator fluid will overflow when the radiator and fluid reach their 95.0∘C operating temperature, given that the fluid’s volume coefficient of expansion is 600×10−6/∘C? Note that this coefficient is approximate, because most car radiators have operating temperatures of greater than 95.0∘C.

Answer 1

ΔV = 0.816 L

Step-by-step explanation:

The change in volume of the fluid upon heating is given by the following formula:

ΔV = βVΔT

where,

ΔV = Increase in Volume of Fluid = Volume of Overflow = ?

β = Coefficient of volumetric expansion of fluid = 600 x 10⁻⁶ °C⁻¹

ΔT = Change in Temperature = Final Temperature - Initial Temperature

ΔT = 95°C - 10°C = 85°C

Therefore,

ΔV = (600 x 10⁻⁶ °C⁻¹)(16 L)(85° C)

ΔV = 0.816 L