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$\bullet$ (a) Steel train rails are laid in 12.0 -m-long segments placed end to end. The rails are laid on a winter day when their temperature is $-2.00^{\circ} \mathrm{C}$ . How much space must be left between adjacent rails if they are just to touch on a summer day when their temperature is $33.0^{\circ} \mathrm{C} ?$ (b) If the rails are mistakenly laid in contact with each other, what is the stress in them on a summer day when their temperature is $33.0^{\circ} \mathrm{C}$ ?

5.0 $\mathrm{mm}$$-8.4 \times 10^{7} \mathrm{Pa}($ compressive $)$

Physics 101 Mechanics

Chapter 14

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

Cornell University

Hope College

University of Sheffield

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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everyone. This is Question number 10 from Chapter 14. This problem is about train tracks being laid and were given an initial length that they're laid in 12 meter sections and initial temperature night of two degree C and then, for part, a space needed between if there just to touch at 33 degrees Celsius and B if in contact when laid. What is the stress in the tracks at 32 33 degrees C? So for part A, we have initial length. We have initial temperature, were given a final temperature, and we need how much length between them, so he essentially needed Delta l. So we should be thinking thermal expansion, which were given a crazy in the book Delta L equals l not Alfa Delta team. So we're given all these things were given l not We can find an Alfa and we're given adult a T so we can just plug these in and solve for and saw for the delta l which would be the space that is needed. So 12 meters, which is our l not are awful for steals 1.2 times 10 to the minus five and then our change in temperature is 33 minus negative to which ends up being 35. And if you plug that in, you get a Delta L of five millimeters. That's the space union between the tracks. Okay, So for part B, if they are in contact, what is the stress? So now stresses force. We should be thinking thermal stress s and were given again In the textbook, stress is equal to minus gamma Alfa Delta team plug in our numbers minus gamma for steals two times 10 to the 11th Pascal's alsa 1.2 times 10 to the minus five for steel and then delta T We just determined his 35 degrees C. And if you plug that into your calculator, you get minus 8.4 times 10 to the seventh pass cows and our minus sign here means that the force distress is compressed compressive. So you might be thinking, I thought our question for stress wass minus Alfa minus a, which is area Alfa Gamma Alpha Delta team. But stress is a pressure, not a force, and four in pressure equals force over area. So we divide this. This is we divide this a over to the other side. T enforce over area, which is pressure, which leaves us with minus alpha delta T mice Gamma Alpha Delta T Excuse me.

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