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(II) The density of water at $4^{\circ} \mathrm{C}$ is $1.00 \times 10^{3} \mathrm{kg} / \mathrm{m}^{3} .$ What is water's density at $94^{\circ} \mathrm{C} ?$ Assume a constant coefficient of volume expansion.

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$D_{\text {final}}=981.45 \mathrm{kg} / \mathrm{m}^{3}$

Physics 101 Mechanics

Chapter 17

Temperature, Thermal Expansion, and the Ideal Gas Law

Temperature and Heat

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the density of water at four degrees else's is one times 10 to 3 kilograms meters cube. What is waters density at 94 degrees Celsius? Seem a constant coefficient of volume expansion. Say the trick with this is is Thio realize that the approximation we're making keeps the mass as constant. So it's just changing the volume, and that's going to be what changes the density. So, um, then delta the eat. So the Bridge of Ray of Density, it will let let's just go with density is equal thio um current density. So, uh, yeah. Okay, so let's go with the end for the new density d over the original density. Um on dhe is, uh, multiplied by the change off temperature. What is most point by, um, one over, um, one plus the change off volume. Now, the change of volume is simply given by by the, uh, the temperature rate of expansion temperature dependent rate of expansion times by. Actually, you don't need to use the times, but in this case, because it's algebra, um, so multiplied by the Dota t say so. This is going to give us on new density. So we're taking the original density and times in Bonnie proportionally the change in volume here. So So this is going to say that, uh d and is equal. Thio one times 10 jude divided by one plus delta The in this case, Delta V for water is given by no point nor no to not to what, um say not. Point Not not No. 21 on the change in the change in the change in temperature is clearly 90 minus for which gives us morning tea. Popping that into a calculator online calculator quickly gives us our final density, which is 981 0.45 so d and equals 940 Fine. Point me, Just don't change that. 981.45 Sorry. 981 Getting the wrong way around 981.45 on Let's not forget our unit of measurement here. So densities in kilograms per me Too cute

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