A 100. mm by 100. mm by 5.00 mm block of ice at 0 degrees C is placed on its fla

Question

A 100. mm by 100. mm by 5.00 mm block of ice at 0 degrees C is placed on its flat face on a 10.0-mm-thick metal desk that covers a pot of boiling water at normal atmospheric pressure. The time needed for the entire ice block to melt is measured to be .400 s. The density of ice is 920. kg/m^3. Use the data in Table 18.3 to determine the metal the disk is most likely made of.

Table 18.3: Some Representative Thermal Conductivities

Materials                                 k[W(m/K)]

Copper                                     386

Aluminum                                 220

Concrete                                      0.8

Glass                                            0.8

Rubber                                         0.16

Wood                                           0.16

Explanation / Answer

Volume of the ice block V = 100 mm x 100 mm x 5 mm                                          = 50000 mm 3                                          = 50000 x 10 -9 m 3 Density = 920 kg / m 3 Mass of the block m = V                                  = 0.046 kg Time t = 0.4 s Thickness of the plate L = 10 mm                                       = 10 -2 m Amount of heat required to melt the ice Q = mL ' Where L ' = Latent heat of fusion of ice                  = 334.88 x 10 3 J / kg Temperature difference d = 100 - 0                                           = 100 o C Area A = 100 mm x 100 mm              = 10 4 mm 2              = 10 4 x 10 -6 m 2         We know Q = KA d t /L From this K = QL / [A d t ] Subsitute values we get K = 385.113 W / m K So, the metal is COPPER

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