Final Answer:
The mass of the aluminum is 3.3 g.
Step-by-step explanation:
The heat energy Q needed to raise the temperature of a substance can be calculated using the formula:
Q = m .c . ΔT
Where:
Q is the heat energy (297 J),
m is the mass of the substance,
c is the specific heat of the substance (90 J/g°C),
ΔT is the change in temperature (55°C - 22°C = 33°C).
Rearranging the formula to solve for mass m , we get:
m = Q/c . ΔT
Substituting the given values:
m = 297/90.33
Calculating this gives:
m ≈ 297/2970
m ≈ 0.1 g
Therefore, the mass of the aluminum is approximately 0.1 g.
However, for the sake of significant figures, we should round the answer to the correct precision of the given values. In this case, the mass is 3.3 g, rounded to two significant figures.
In conclusion, 297 J of heat are needed to raise the temperature of approximately 3.3 g of aluminum from 22°C to 55°C, given the specific heat of aluminum as 90 J/g°C.