A person with a body mass of 70 kg owns a pair of ice skates, each of which has

Question

A person with a body mass of 70 kg owns a pair of ice skates, each of which has a knife edge 0.5 mm wide and 20 cm long. Assume that ice skating involves gliding on a thin film of water and that the thermodynamics of bulk water apply to this case.

a. Calculate the minimum temperature of the ice on which the person can go skating. At 0 C and 1 atm pressure the densities of ice and liquid water are 0.917 g cm-3 and 0.9998 g cm-3, respectively.
b. Comment on the validity of the result relative to your own experience.

Explanation / Answer

m = 70 kg

W = mg = 70*9.8 = 686 N

A = l*h = (0.5*10^-3)(20*10^-2) = 0.0001 m2

P = W/A = 686/0.0001 = 6860000 Pa

2 shopes in pair = 6860000/2 = 3430000 Pa = 33.85 atm

so..

a) T min in which ice remains Ice

dP/dT = dHfus/dTfus*dVm

dT = dP*dVm*Tfus/(dHfus)

T2-T1 = (P2-P1)*(V2-V1)*Tf / Hfus

V2-V1 = 1/0.917 - 1/0.9998 = 0.090312 cm3/g

to molar

0.090312 cm3/g * 18 g /mol * (1 m / 100 cm)^3 = 0.00000162 m3/mol

T2 = 273.15 + (33.85 -1) * (0.00000162)* (273.15)/(6.008*10^3)

T2 = 273.1500°C

b)

this is valid only when Pressure is exerted, in any casein which the pressure is not on, this will not be valid

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