Question

Answer the following questions:

a) In 1992, 1.804 * 10 ^ 6 kg of silver was produced in the United States. What mass of ice must be melted so that this mass of liquid silver can solidify? Assume that both substances are brought into contact at melting temperatures. The latent heat of fusion for silver is 8.82 * 10 ^ 4 J / kg.

b) The lowest temperature measured on the surface of a planetary body in the solar system is that of Triton, the largest of Neptune's moons. The surface temperature on this distant moon can reach a low of -235 C. Suppose an astronaut brings a water bottle containing 0.500 kg of water to Triton. The water's temperature decreases until it freezes, then the temperature of the ice decreases until it is in thermal equilibrium with Triton at a temperature of -235 C. If the energy transferred by heat from the water to Triton is 471 kJ, what is the value of the water's initial temperature?

Answer 1

a)

m = mass of ice melted = ?

M = mass of silver solidified = 1.804 x 10⁶ kg

L_s = latent heat for silver = 8.82 x 10⁴ J/kg

L = latent heat for ice = 334 x 10³

using conservation of heat

Heat gained by ice = heat lost by silver

mL = M L_s

m (334 x 10³ ) = (1.804 x 10⁶) (8.82 x 10⁴)

m = 4.76 x 10⁵ kg

b)

T_i = initial temperature = ?

T = final equilibrium temperature = - 235

Q = heat transferred = 471000 J

L = latent heat = 334 x 10³ J/kg

m = mass of water = 0.5 kg

c_w = specific heat of water = 4186

c_i = specific heat of ice = 2093

using conservation of heat

Q = mc (T_i - 0) + mL + m c_i (0 - T)

471000 = (0.5) (4186) T_i + (0.5) (334 x 10³) + (0.5) (2093) (0 -(-235))

T_i = 27.75