3960 J of heat are added to a 27.6 g sample
of iron at 25
◦
C. What is the final temperature of the iron? The specific heat of iron is
0.449 J/g · K.
Answer in units of K
1)Convert 25* Celsius to Kelvin.
Celsius + 273.15 = Kelvin
Plug the given numbers in this formula and solve for final temperature.
q = mcΔT
where
q = heat energy
m = mass
c = specific heat
ΔT = change in temperature = final temperature - initial temperature
To find the final temperature of the iron, we can use the formula:
q = m * c * ΔT
where:
q = heat transferred
m = mass of the sample
c = specific heat capacity
ΔT = change in temperature
Given:
q = 3960 J
m = 27.6 g
c = 0.449 J/g · K
ΔT = ?
To solve for ΔT, we need to rearrange the formula:
ΔT = q / (m * c)
Substituting the given values:
ΔT = 3960 J / (27.6 g * 0.449 J/g · K)
Simplifying:
ΔT = 3960 J / (12.3924 g · J/g · K)
ΔT ≈ 319.78 K
Therefore, the final temperature of the iron is approximately 319.78 K.
To find the final temperature of the iron, we can use the formula for heat:
Q = m × C × ΔT
where:
Q = Heat energy (in Joules)
m = Mass of the substance (in grams)
C = Specific heat capacity of the substance (in J/g · K)
ΔT = Change in temperature (in Kelvin)
In this case, we know the heat energy added (Q = 3960 J), the mass of the iron (m = 27.6 g), and the specific heat capacity of iron (C = 0.449 J/g · K). We need to find the change in temperature (ΔT).
Rearranging the formula, we have:
ΔT = Q / (m × C)
Calculating:
ΔT = 3960 J / (27.6 g × 0.449 J/g · K)
ΔT ≈ 32.2 K
Now, we can find the final temperature by adding the change in temperature to the initial temperature:
Final temperature = Initial temperature + ΔT
The initial temperature is given as 25 ◦C. Converting it to Kelvin:
Initial temperature (in K) = 25 ◦C + 273.15
Final temperature = 25 ◦C + 32.2 K
Final temperature ≈ 307.2 K
Therefore, the final temperature of the iron is approximately 307.2 K.