Question

Chapter 13

Problem 13.16

3 of 15

Constants It is observed that 55.20 mL of water at 20?C completely fills a container to the brim. When the container and the water are heated to 60?C, 0.35 g of water is lost.	Part A What is the coefficient of volume expansion of the container? Density of water at 60 ?C is 0.98324 g/mL. Express your answer using two significant figures. ?container = 1/?C SubmitRequest Answer Part B What is the most likely material of the container? What is the most likely material of the container? aluminum copper glass iron SubmitRequest Answer Provide Feedback Next

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Answer 1

Part-A

Volume lost of water(dV) = volume expand of water(dVw) - Volume expand of container(dVc)

here, Expansion in volume due to temperature change is given by,

dV = *V0*dT

So, expansion in volume of container = dVc = c*Vc*dT

expansion in volume of water = dVw = w*Vw*dT

given, Vc = Vw = volume of water or container = 55.20 ml = 0.0552 Ltr = 5.52*10^-5 m^3

dT = change in temperature = 60 degC - 20 degC = (60 - 20) degC = 40 degC

c = Coefficient of volumetric expansion of container = ??

w = Coefficient of volumetric expansion of water = 207*10^-6

dV = 0.35 g water = (0.35/density of water at 60 degC) = 0.35/0.98324 = 0.356 ml = 3.56*10^-7 m^3

So, amount of coffee spilled out of the beaker = dV = dVw - dVc

dV = (w - c)*V0*dT

3.56*10^-7 = (207*10^-6 - c)*(5.52*10^-5)*40

(207*10^-6 - c) = (3.56*10^-7)/(40*5.52*10^-5)

c = 207*10^-6 - (3.56*10^-7)/(40*5.52*10^-5)

c = 4.58*10^-5 1/degC = coefficient of volume expansion of the container

Part B.

Using reference data, this material is most likely to be copper.

Therefore answer is option B.