Question

Answer the following questions:

a) Lake Superior contains about 1.20 * 10 ^ 16 kg of water, whereas Lake Erie contains only 4.8 * 10 ^ 14 kg of water. Suppose aliens use these two lakes for cooking. They heat Lake Superior to 100 C and free Lake Erie to 0.0 C. Then they mix the two lakes together to make a "lake shake." What would be the final temperature of the mixture? Assume that the entire energy transfer by heat occurs between the lakes.

b) Suppose that an ice palace built in Minnesota in 1992 is brought into contact with steam with a temperature of 100.0 C. The temperature and mass of the ice palace are 0.0 C and 4.90 * 10 ^ 6 kg, respectively. If all of the steam liquefies by the time all of the ice melts, what is the mass of the steam?

c) The United States Bullion Depository at Fort Knox, Kentucky, contains almost half a million standard mint gold bars, each with a mass of 12.4414 kg. Assuming an initial bar temperature of 5.0 C, each bar will melt if it absorbs 2.50 MJ of energy transferred by heat. If the specific heat capcity of gold is 129 J / kg * C and the melting point of gold is 1063 C, calculate the heat of fusion of gold.

Answer 1

Given is:-

T_E = 0 degree C

T_S = 100 degree C

L_f of ice =

Q_S = energy transferred by heat from Lake Superior

Q_E = energy transferred by heat to Lake Erie

From the conservation of energy

Q_S = Q_E

Thus the Final temperature of the mixture is 92.9 degree celcius.