Sapling learning You happen to come across a piece of metal which has a density

Question

Sapling learning You happen to come across a piece of metal which has a density of p 37.20 g/cm when the temperature is To E 55.0 °C. If the metal is cooled to a temperature of T1 E 0.00 °C does the density change? Yes, since the metal contracts and the mass is constant the density will increase. o Yes, the density will decrease since the volume changes O No, density does not depend on temperature No, because as the volume changes so does the mass Calculate the density of the piece of metal at this temperature, p1. The coefficient of volume expansion for this piece of metal is B-7.35 x105 1/oC. Number g/ cm

Explanation / Answer

here,

Yes the density is increased,

as the metal contracts and the mass is same,

density = mass/volume

beta = 7.35 * 10^-5 degree C^-1

let the mass of the metal be m

initial volume , V0 = m /7.2 cm^3

let the change in volume be V'

beta = V'/( V0 * delta T)

7.35 * 10^-5 = V' /( ( 0 - 55) *m /7.2 )

V' = - 56.15 * m * 10^-5

final volume , Vf = V0 + V'

Vf = m*(0.139 - 56.15 * 10^-5 )

Vf = 0.1384 * m cm^3

final density , pf = m /( 0.1384 * m)

pf = 7.22 g/cm^3

the new density of the metal is 7.22 g/cm^3

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