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A geodesic dome constructed with an aluminum framework is a nearly perfect hemisphere; its diameter measures 55.0 $\mathrm{m}$ on a winter day at a temperature of $-15^{\circ} \mathrm{C}$ . How muchmore interior space does the dome have in the summer, when the temperature is $35^{\circ} \mathrm{C}$ ?

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The excess in the Volume $={160 \mathrm{m}^{3}}$

Physics 101 Mechanics

Chapter 14

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

Cornell University

University of Washington

Simon Fraser University

McMaster University

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.

0:00

A geodesic dome constructe…

02:16

05:10

A geodesic dome const…

01:11

Exercise 17.16Constant…

03:37

A metallic sphere cools fr…

02:45

01:40

A sphere that is a perfect…

02:44

Suppose that a steel hoop …

Let's take a look at the question question was asking us how much for more interior space doesn't don't have. Okay, well well, we know extra space is able to the change bottom. Here she is talking about spaces of honor. So after Spain, Ming's the different between the fine, no Valium and the initial ball, which is a change one will be equal to the extra space And how we go to beta. Which the court fishing off. What? Expansion of alumina times the initial volume and ties the change in temperature. Okay, why is the condition of foreign expansion off aluminum is because this ah looming a framework. Okay, so the materials aluminum. So while it's for car capitation, I'm from table 14 going to you know that the conditions equal to 7.2 times 10 donated by over the resources we know you want Even Waas. We don't know. Sorry. I actually don't know. OK, but we can How? Remember? We know the diameter. Okay, which is 55 meter. So radio is if I You are right to wishes to 27.5 Peter. Okay. And the volume for hemisphere because remember, looking on framework in this question is the ham suit. Okay, so it's 1/2 severe, which is so the one employees just to over three times player So cute. Okay, she's is one. Have. So because the bottom off the spheres over three times pi r q. So for hemisphere. So you just simply dividing off the hamstrings. But by two, which is two or three times Pi has argue every blogging number this well, give us 203 has pied has Archie, which is 27.5 meter que and they will give us 4 43,000 456 when I meet you. So let's look volume for the alumina alumina framework initially. Okay, so this is this is the initial bar. Okay, so let's go jump from next page. So we know that on a t is he going to teach you? Mine is t one, which is the final temperatures of 35 degrees Celsius minus negative 15 degrees Celsius, which will give us 50 degrees Celsius. Okay, Not is planning about it since we know all when you whether it's necessary to people the change apart. So start a p equals Who paid a standpoint to has changed a part of magnify over degree Celsius past the initial volume, which is for three by 56 or nine. You don't you times change in temperature, which is 50 degree Celsius, and this will give us the changing going. Oh, the actual airspace is equal to It's really close, like 1 60 Mira que there's my healthy. The exact answer because I running up and he's about 1 60 meter to and you can leave the answer like there. Okay, so that's my answer. His question. Thank you.

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