.100 KG piece of metal is heated to 480°C and then quickly place in .250 KG of water at 20°C which is contained in a .200 KG aluminum calorimeter the final temperature of the water metal and calorimeter is 36°C what is the specific heat to Capacity of the metal piece
See your other H2O/Cu/Al problem just above.
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To find the specific heat capacity of the metal piece, we can use the principle of conservation of energy. The heat gained by the water and calorimeter is equal to the heat lost by the metal piece.
Let's calculate the heat gained by the water and calorimeter and the heat lost by the metal piece.
1. Heat gained by water and calorimeter:
The specific heat capacity of water is approximately 4.18 J/g°C.
The mass of water is 0.250 kg, and the change in temperature is (36°C - 20°C) = 16°C.
So, the heat gained by the water is:
Qwater = (mass of water) * (specific heat capacity of water) * (change in temperature)
= 0.250 kg * 4.18 J/g°C * 16°C
The specific heat capacity of aluminum is approximately 0.897 J/g°C.
The mass of the calorimeter is 0.200 kg, and the change in temperature is also 16°C.
So, the heat gained by the calorimeter is:
Qcalorimeter = (mass of calorimeter) * (specific heat capacity of aluminum) * (change in temperature)
= 0.200 kg * 0.897 J/g°C * 16°C
2. Heat lost by the metal piece:
The change in temperature of the metal piece is (36°C - 480°C) = -444°C.
To convert the negative change in temperature to positive, we need to take the absolute value.
So, the change in temperature of the metal piece is 444°C.
The heat lost by the metal piece is:
Qmetal = (mass of metal) * (specific heat capacity of metal) * (change in temperature)
= 100 kg * (specific heat capacity of metal) * 444°C
According to the principle of conservation of energy, the heat gained by the water and calorimeter is equal to the heat lost by the metal piece:
Qwater + Qcalorimeter = Qmetal
Now we can solve for the specific heat capacity of the metal piece:
100 kg * (specific heat capacity of metal) * 444°C = 0.250 kg * 4.18 J/g°C * 16°C + 0.200 kg * 0.897 J/g°C * 16°C
Simplifying the equation and solving for the specific heat capacity of the metal:
(specific heat capacity of metal) = (0.250 kg * 4.18 J/g°C * 16°C + 0.200 kg * 0.897 J/g°C * 16°C) / (100 kg * 444°C)
Performing the calculations:
(specific heat capacity of metal) = 59.864 J/kg°C
Therefore, the specific heat capacity of the metal piece is approximately 59.864 J/kg°C.