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$\cdot$ A metal rod is 40.125 $\mathrm{cm}$ long at $20.0^{\circ} \mathrm{C}$ and 40.148 $\mathrm{cm}$ long at $45.0^{\circ} \mathrm{C} .$ Calculate the average coefficient of linear expansion of the rod's material for this temperature range.

$2.29 \times 10^{-5} C^{-1},$ click to see the steps

Physics 101 Mechanics

Chapter 14

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

University of Michigan - Ann Arbor

University of Washington

Hope College

Lectures

02:20

A solid, liquid, or gas is one of the three main states of matter. Solids have a definite shape and volume, and retain their shape when a force is applied to them. They are rigid, and do not flow to take on the shape of a container, but retain their own shape. Solids are held together by intermolecular forces, which are usually chemical bonds. Liquids have a free-flowing, continuous surface, and take the shape of a container. They flow to fill an available space. Their particles do not have a definite shape or volume, and they are not rigid. Gases have no definite shape or volume. They are not held together, and are not rigid. They flow to fill an available space. Gases are often described as being the state of matter with the lowest density.

03:25

The First Law of Thermodynamics is an expression of the principle of conservation of energy. The law states that the change in the internal energy of a closed system is equal to the amount of heat energy added to the system, minus the work done by the system on its surroundings. The total energy of a system can be subdivided and classified in various ways.

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I guess let's take a look at the question, so the question was asking us to figure out the average coefficient reading expansion of the rawest material for this temporary range. So well. We know that delta l, which is l 2 minus 1, which is the final lent. The initial length is equal to the initial length times the linear coefficient of expansion times the changing temperature, which is 2 minus 1, also in an out turned delta t. So that means alpha, which is a linear expansion. Adding the coefficient of the expansion is just simply equal to delta l, over l, 1 divided by delta t and delta l. Just l, 2 minus l, 1 l 1 is l. 1 delta t is t 2 minus t 1 point: okay, let's jump to the next page since it's come crowdy here. So alpha is equal to l 2 minus l, 1 divided by l 1 times. T 2 minus t 1 remember to l. 1 was given t 2 and t 1 is given as well as that's plugging the value which is equal to 40.128 centimereminus 40.125 centimeter divided by l 1, which is 40.125 centimeter times, t 2 minus done, which is 45 degree celsius, minus 20 degrees celsius. And in this case we don't give convert the centimeters meter, because eventually the unit centimeter would cancel out. So you would just leave the bunch of digits into it without unity, so let's keep doing it and the other linear coefficient of expansion should be equal to 2.29 times 10 to the negative 10 to the power of negative 5 over degrees celsius. And that's the answer for this question. Thank you.

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