Question

A 0.4 kg piece of ice at -19 ∘C is dropped from a height h. Upon impact, 6 % of its kinetic energy is converted into heat energy.

If the impact transforms all of the ice into water that has a final temperature of 0 ∘C, find h.

Express your answer in meters to two significant figures.

Answer 1

Kinetic Energy gained by ice just before impact is given by,

KE = m*g*h

here, m = mass of ice = 0.4 kg

g = 9.81 m/sec^2

h = ??

Energy required for converting -19 degC ice to 0 degC water is given by,

Q = m*C*dT + m*L

here, C = specific heat of ice = 2108 J/kg-K

dT = change in temperature = 0 - (-19) = 19 degC

L = Latent heat of fusion of ice = 334 J/gm = 3.34*10^5 J/kg

So, Q = 0.4*2108*19 + 0.4*3.34*10^5

Q = 149620.8 J

Energy transfer from kinetic energy to heat energy(E) = 6% of Kinetic energy

E = 0.06*m*g*h

given E = Q

So, h = Q/(0.06*m*g) = 149620.8/(0.06*0.4*9.81) = 635494 m

h = 6.4*10^5 m

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