Question

Part A)

You have 67 grams of a unknown material, and you would like to find out its specific heat. You decide to heat it up to 100 C and put it in a 66 g aluminum cup (specific heat = 0.22 cal/(g C) that 200 grams of water (specific heat = 1 cal/(g C)). Usually this aluminum cup is in another cup so that the system is insulated. If both the cup and the aluminum cup are initially at 20 C, and the equilibrium temperature of the system ends up being 22.5 degrees some time later. What is the specific heat of the material?Part

Part B)

You have 80 grams of water at 80 C, and you put 40 grams of ice at 0 deg C. Eventually, all the ice melts and the system attains an equilibrium temperature of 27 C. What is the latent heat of fusion?

Answer 1

A)
Consider the unknwon specific heat as Cu
Heat lost by unknown material,
Ql = Mu * Cu * dT1
Where Mu is the mass of the unknown material and dT1 is the change in temperature of the unknown material
Substituting values,
Ql = 67 * Cu * (100 - 22.5)
= 5192.5 * Cu

Heat gained by aluminum cup,
Qga = Ma * Ca * dTa
Where Ma and Ca are the mass and specific heat of aluminum, dTa is the change in temperature for aluminum.
Substituting values,
Qga = 66 * 0.22 * (22.5 - 20)
= 36.3 Cal

Heat gained by water,
Qgw = Mw * Cw * dTw
Where Mw and Cw are the mass and specific heat of water, dTw is the change in temperature of water.
Qgw = 200 * 1 * (22.5 - 20)
= 500 Cal

Heat lost by unknown material = Heat gained by aluminum cup + Heat gained by water.
5192.5 * Cu = 36.3 + 500
Cu = 536.3 / 5129.5
= 0.10 cal/g.C

B)
Heat gained by ice during phase change from ice to water,
Qi1 = Mi * Lf
Where Mi is the mass of ice and Lf is the latent heat of fusion of ice.

Heat gained by 0 ^oC water when heated to 27 ^oC,
Qi2 = Mi * Cw * dT1
Where Cw is the specific heat of water and dT1 is the change in temperature of water

Heat lost by water at 80 oC,
Qw = Mw * Cw * dT2
Where Mw is the mass of water and dT2 is the change in temperature for water.

Heat lost by water = Total heat gained by ice
Mw * Cw * dT2 = Mi * Cw * dT1 + Mi * Lf
Substituting values,
80 * 4.814 * (80 - 27) = 40 * 4.184 * (27 - 0) + 40 * Lf
17740.16 = 4518.72 + 40 * Lf
40 * Lf = 13221.44
Lf = 331 J/g