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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 $95.0^{\circ} \mathrm{C}$ .

$V_{\text {ourflow}}=\Delta V=0.544 \mathrm{mL}$

Physics 101 Mechanics

Chapter 13

Temperature, Kinetic Theory, and the Gas Laws

Temperature and Heat

Jeanylle A.

January 17, 2021

why did we subtracted the 2 betas

Rutgers, The State University of New Jersey

University of Michigan - Ann Arbor

Hope College

Lectures

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so we know the change in length for linear expansion would be equal to Alfa. The linear expansion coefficient times the original length times the change in and temperature. The change in volume is very nearly three times Alfa, three times a linear expansion coefficient times the original volume times the change in temperature. This is equaling two beta The volume expansion coefficient times the original volume times Delta T. And so we can say that then the change in length would be equal be volume expansion coefficient beta divided by three multiplied by the original length times the change in temperature. And so we can then say that the change in volume the difference in the change in volume, um would be equaling essentially beta. The volume expansion coefficient for the radiator fluid minus the volume expansion coefficient for copper multiplied by the original volume times Delta T. And so we can then solve and say that this is going to be equaling. This would be 400 minus 51 again taught here it would be times 10 to the negative six per degree Celsius multiplied by the original volume of 16 leaders multiplied by the change in temperature of 95 degrees Celcius, minus 10 degrees Celsius. And so we can write it here. The change in volume would be equaling point 475 leaders. And so this would be our final answer or changing volume is again 0.475 leaders. That is the end of the solution. Thank you for one.

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