2. A 55 g piece of metal is heated to 95° C and placed in a calorimeter that con

Question

2. A 55 g piece of metal is heated to 95° C and placed in a calorimeter that consists of a 50.0 g aluminum cup and 150 g of water at a temperature of 18°C. If the equilibrium temperature of the calorimeter is 23°C, what is the specific heat of the piece of metal? answer 3. A 25 g ice cube is initially at 0.0°C and placed in an insulated cup containing 3.00 x 102 g of water at 20.0°C. What will be the final temperature of the water in the cup! answer 4. How much cold water (T = 5.0°C) must be added to 180 g of hot coffee (T 90°C) to bring the temperature down to 80.0 °C? Assume the coffee has the same specific heat as water. answe

Explanation / Answer

2.

Using Energy conservation:

Heat released by metal = Heat gained by calorimeter and water

Q1 = Q2 + Q3

Q1 = heat released by metal = M*C*dT

M = 55 gm = 0.055 kg & dT = Tf - Ti = 95 - 23 = 72 C

C = specific heat of metal = ?

Q2 = heat gained by aluminum = Ma*Ca*dT1

Ma = 50 gm = 0.05 kg & dT1 = 23 - 18 = 5 C

Ca = specific heat of aluminum = 900 J/kg-K

Q3 = heat gained by water = Mw*Cw*dT1

Mw = 150 gm = 0.15 kg & dT1 = 23 - 18 = 5 C

Cw = specific heat of water = 4186 J/kg-K

Using above values:

0.055*C*72 = 0.05*900*5 + 0.15*4186*5

C = [0.05*900*5 + 0.15*4186*5]/(0.055*72)

C = 849.62 J/kg-K (Ans)

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