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(II) (a) Show that the change in the density $\rho$ of a substance, when the temperature changes by $\Delta T,$ is given by $\Delta \rho=-\beta \rho \Delta T .$ (b) What is the fractional change in density of a lead sphere whose temperature decreases from $25^{\circ} \mathrm{C}$ to $-55^{\circ} \mathrm{C} ?$

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a) $\Delta \rho=-\rho \beta \Delta T$b) 0.70$\%$ increase

Physics 101 Mechanics

Chapter 17

Temperature, Thermal Expansion, and the Ideal Gas Law

Temperature and Heat

University of Michigan - Ann Arbor

University of Sheffield

McMaster University

Lectures

05:50

(II) $(a)$ Show that the c…

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A temperature change $\Del…

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Density is mass divided by…

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A liquid has a density $\r…

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A sample of a solid substa…

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The coefficient of volume …

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01:40

A solid substance has a d…

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A sphere of mass $\mathrm{…

04:34

(a) When cooled, the densi…

03:52

The temperature increase o…

no Delta Rho. The change in density is final density Manus Initial density that mass by final volume minus mass By initial volume, we know that volume changes as we're not into one place. Pita Daddy. So Linus, and by me not we can write this us And by B not times one by one press pita t beat Beat a little dirty minus one. This is We know that and I were not is wrong. So that's wrong. Not times Beetle Daddy by one place. I'm sorry. Minus Peter. Tell Daddy buy one hospital, Daddy. Because, Peter, that is where his fall. We can ignore this in compassion Toe one. And we can write this us minus Peter Delta t drawn up. So that's the proof for Eldorado called Minus Peter Delta T donut for Bobby. You know that the temperature went from 25 degrees to minus 55 degrees, so don't have overt rule is minus Peter. Tell Daddy which is minus a day. So on into tend bar minus six. I'm minus 55 minus 25 which is 6.96 into a tent bar ministry, which is 0.70% increase

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