Most automobiles have a coolant reservoir to catch radiator...

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 $\beta=400 \times 10^{-6} /^{\circ} \mathrm{C} ?$ Note that this coefficient is approximate, because most car radiators have operating temperatures of greater than $95.0^{\circ} \mathrm{C}$ .

Labs

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

Key Concepts

Thermal Expansion

Thermal expansion is the tendency of matter to change its volume in response to a change in temperature. When a substance is heated, its molecules move more vigorously and typically occupy a larger volume. This principle is crucial in many practical applications, including automotive cooling systems, where materials and fluids expand as the engine heats up.

Coefficient of Volume Expansion

The coefficient of volume expansion (?) quantifies the change in volume per unit volume per degree change in temperature. It is a material-specific property that helps predict how much a liquid or solid will expand with a given increase in temperature. This parameter is essential in calculations involving the expansion of fluids, such as in the problem where the radiator fluid's expansion causes overflow.

Temperature Change

Temperature change is the difference between the final and initial temperatures, and it directly influences the extent of thermal expansion. In expansion problems, the magnitude of the temperature change drives the overall change in volume when multiplied by the relevant coefficient of expansion, illustrating how heating can impact system capacities and safety measures.

Transcript

Please give Ace some feedback