Question

It is observed that 56.00 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.

Part B

What is the most likely material of the container?

copper

aluminum

glass

iron

Answer 1

Expansion in volume due to temperature change is given by,

dV = *V0*dT

So, expansion in volume of container = dVb = c*V0*dT

expansion in volume of water = dVc = w*V0*dT

given, V0 = volume of container = 56.00 ml = 56*10^-6 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 = 210*10^-6

amount of water spilled out of the beaker = 0.35 g

then, dV = 0.35/0.98324 = 0.356 ml = 0.356*10^-6 m^3

So,

0.356*10^-6 = (w - c)*56*10^-6*(60 - 20)

c = 210*10^-6 - (0.356*10^-6)/[(56*10^-6)*40]

c = 5.1*10^-5 1/degC

Part-B.

Since, Coefficient of volumetric expansion of Copper = 5.1*10^-5 1/degC

So, the most likely material of the container is Copper.

Correct option is A.

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