1kg of an unknown metal at 94 degrees C is placed in 100g of water at 10 degrees C. The final temperature of the metal and water are 17 degrees C. By finding specific heat capacity, identify the metal
To identify the metal, we can make use of the principle of conservation of energy, specifically the principle of heat transfer.
The principle of heat transfer states that the amount of heat gained by one object is equal to the amount of heat lost by another object during a heat transfer process.
In this case, the unknown metal is initially at 94 degrees C and is brought into thermal contact with the water at 10 degrees C. Heat will be transferred from the metal to the water until they reach a common final temperature of 17 degrees C.
The heat lost by the metal can be calculated using the formula:
Q = mcΔT
Where:
Q = heat lost by the metal
m = mass of the metal (1 kg)
c = specific heat capacity of the metal
ΔT = change in temperature of the metal (94 - 17 = 77 degrees C)
The heat gained by the water can be calculated using the same formula:
Q = mcΔT
Where:
Q = heat gained by the water
m = mass of the water (100 g)
c = specific heat capacity of water (4.18 J/g°C)
ΔT = change in temperature of the water (17 - 10 = 7 degrees C)
Since the amount of heat lost by the metal is equal to the amount of heat gained by the water, we can equate the two equations:
mcΔT = mcΔT
Simplifying the equation by canceling out the masses and rearranging, we get:
c (metal) = (mcΔT)/(mcΔT)
The masses and temperature changes cancel out on both sides, leaving us with:
c (metal) = c (water)
Therefore, the specific heat capacity of the metal is equal to the specific heat capacity of water, which is 4.18 J/g°C.
This indicates that the metal is likely to be aluminum, as its specific heat capacity is very close to that of water (around 0.896 J/g°C).