A 100 g sample of aluminum (c = 0.903 J/g°C) and a 100 g sample of iron (c = 0.449 J/g°C) are both heated from 20.2°C to 65.8°C. Which statement correctly describes the amount of heat that is absorbed?
a) It is the same for both samples.
b) It is greater for the aluminum than for the iron.
c) It is greater for the iron than for the aluminum.
d) It is twice as great for the iron than for the aluminum
e) It cannot be determined.
To determine the amount of heat absorbed by each sample, we can use the formula:
Q = mcΔT
Where:
Q = the amount of heat absorbed
m = mass of the sample
c = specific heat capacity of the material
ΔT = change in temperature
For the aluminum sample:
Q(aluminum) = (100 g)(0.903 J/g°C)(65.8°C - 20.2°C)
Q(aluminum) = (100 g)(0.903 J/g°C)(45.6°C)
For the iron sample:
Q(iron) = (100 g)(0.449 J/g°C)(65.8°C - 20.2°C)
Q(iron) = (100 g)(0.449 J/g°C)(45.6°C)
By evaluating these equations, we find that the amount of heat absorbed is the same for both samples.
Therefore, the correct statement is:
a) It is the same for both samples.
is a) the final answer?
Yes, the correct answer is a) It is the same for both samples.
To determine the amount of heat absorbed by each sample, we can use the formula:
Q = mcΔT
Where Q represents the amount of heat absorbed, m is the mass of the sample, c is the specific heat capacity of the material, and ΔT is the change in temperature.
For the aluminum sample:
m = 100 g
c = 0.903 J/g°C
ΔT = (65.8°C - 20.2°C) = 45.6°C
Q_aluminum = (100 g) * (0.903 J/g°C) * (45.6°C)
Similarly, for the iron sample:
m = 100 g
c = 0.449 J/g°C
ΔT = (65.8°C - 20.2°C) = 45.6°C
Q_iron = (100 g) * (0.449 J/g°C) * (45.6°C)
Calculating these values:
Q_aluminum ≈ 4109.92 J
Q_iron ≈ 2054.08 J
Comparing the values, we find that the amount of heat absorbed by the aluminum (4109.92 J) is greater than that absorbed by the iron (2054.08 J).
Therefore, the correct statement is:
b) It is greater for the aluminum than for the iron.