Question

A piece of aluminum of mass 1 kg is heated to 100°C and then placed in 0.4 kg of water at 20°C. If the mixture reaches a temperature of 60°C, what is the specific heat capacity of the aluminum if that of water is 4200 J/kg?

Answer 1

The specific heat capacity of the aluminum is determined to be 1680 J/kg°C by using the principle of conservation of energy and the formula Q = mcΔT, taking into account the heat gained by the water and the heat lost by the aluminum.

Step-by-step explanation:

To find the specific heat capacity of aluminum, we can use the principle of conservation of energy, which implies that heat lost by the aluminum will be equal to the heat gained by the water, assuming no heat is lost to the surroundings. The heat lost or gained is given by the formula Q = mcΔT, where Q is the heat transferred, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

1. Determine the change in temperature for both substances:
   
   For aluminum: ΔT = final temperature - initial temperature = 60°C - 100°C = -40°C.
   
   For water: ΔT = 60°C - 20°C = 40°C.
2. Calculate heat transferred to the water using water's specific heat capacity (given as 4200 J/kg°C):
   Qwater = mwatercwaterΔTwater = 0.4 kg * 4200 J/kg°C * 40°C = 67200 J.
3. According to the conservation of energy, the heat lost by the aluminum is equal to the heat gained by the water:
   Qaluminum = Qwater
4. We know the mass of the aluminum and the change in its temperature. We can now calculate its specific heat capacity:
   caluminum = Q / (maluminumΔTaluminum)
   caluminum = 67200 J / (1 kg * -40°C) = -1680 J/kg°C.
   
   The negative sign indicates the direction of heat flow (lost heat), but for specific heat capacity, we use the absolute value.

The specific heat capacity of the aluminum is 1680 J/kg°C.