Three equal masses of metal shot (aluminum, steel, and lead) are heated in boiling water, dumped into equal masses of room temperature water and stirred. The final temperature of each is read with a large display thermometer. Reasonable figures for the heat capacities of the metals can be obtained from the data.
Let the cans of metal shot sit in the boiling water bath for at least ten minutes. Even though the water will be at 100°C, the metal shot will always be slightly cooler due to heat losses between the water and the cans, and between the cans and the metal shot inside.
Mass of water: 80 grams
Mass of each metal: 120 grams
Specific heat of water: Cw = 4.186 J/g·°C
Example 1: 120 grams of aluminum is heated in a water bath to a temperature of 87.3°C. It is poured into 80 grams of water at 20°C. The metal/water combination stabalizes at 38.3°C. Find the specific heat of the aluminum:
mAl ΔTAl CAl = mw ΔTw Cw
(120 grams)(87.3°C - 38.3°C) CAl = (80 grams)(38.3°C - 20°C)(4.186 J/g·°C)
CAl = 1.04 J/g·°C. (Published value: 0.92 J/g·°C).
Example 2: 120 grams of steel is heated in a water bath to a temperature of 88.4°C. It is poured into 80 grams of water at 20°C. The metal/water combination stabalizes at 31.2°C. Find the specific heat of the steel:
msteel ΔTsteel Csteel = mw ΔTw Cw
(120 grams)(88.4°C - 31.2°C) Csteel = (80 grams)(31.2°C - 20°C)(4.186 J/g·°C)
Csteel = 0.55 J/g·°C. (Published value: 0.51 J/g·°C for mild steel).
Example 3: 120 grams of lead is heated in a water bath to a temperature of 89.1°C. It is poured into 80 grams of water at 20°C. The metal/water combination stabalizes at 24.0°C. Find the specific heat of the lead:
mPb ΔTPb CPb = mw ΔTw Cw
(120 grams)(89.1°C - 24.0°C) CPb = (80 grams)(24.0°C - 20°C)(4.186 J/g·°C)
CPb = 0.17 J/g·°C. (Published value: 0.125 J/g·°C).