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$\cdot$ A copper cylinder is initially at $20.0^{\circ} \mathrm{C}$ . At what temperature will its volume be 0.150$\%$ larger than it is at $20.0^{\circ} \mathrm{C}$ ?

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$T_{2}=49.4 \mathrm{C}^{\circ}$

Physics 101 Mechanics

Chapter 14

Temperature and Heat

Thermal Properties of Matter

The First Law of Thermodynamics

Rutgers, The State University of New Jersey

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 12 from chapter 14. And this problem? We're given a copper cylinders at an initial temperature of 20 degrees Celsius and were asked to find temperature when the volume is 0.15 degree percent larger. Okay, so we're talking about volume, and we have temperatures, so we should be thinking thermal expansion. So volume expansion. So we need our coefficient volume expansion for a copper, which is equal, tio 5.1 times 10 to the negative five. Okay, so now I can write out our equation for volume expansion, which is Delta V is equal Tio V, not beta Delta t. So we're solving for del titty. And when you're looking at this, we don't have V nod, but we do have a Delta bi because we're asked to find it when volume is your 0.15 times larger. So that means that Delta V is going to be equal to V not times 0.15 and then this is a percentage. So we have to move the decimal place over to or divide by 100. So your 1000.15 times 10 to the minus two. So we do actually have an expression for Delta Bean, and we can go ahead and solve this equation for Delta T. So Delta T is equal Tio Delta v over ve not beta. And if you see, we have Delta v appear and we have be not over here so we can go back over to this expression that we wrote for Delta V. Divide v not over. And we get Delta V over V not equals 0.15 times 10 to the minus two. So we have it. We have a number for that expression and we have beta. So this just becomes Delta V over V, not over beta, and we can plug in our numbers. Still, tha t equals 0.15 times 10 to the minus two over beta, 5.1 times 10 to the minus five C degrees, the minus one. And if you plug that into your calculator, you get a change in temperature. Delta T Delta T of 29.4 degrees C. That's our Delta T, though that's not our final answer. So now we need to have se t f equals t I, which was 20 plus Delta T she was 29.4, So now our T F equals 49.4 degrees C. So that's the temperature of the copper cylinder when the volume is 0.15% larger.

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