A 23.7 g piece of iron at 54.9°C is cooled and releases 338 J of heat. The specific heat of iron is 0.450 J/g°C. What is the final temperature of the iron? a 13.7°C b 27.9°C c 23.2°C d 31.8°C
Question
A 23.7 g piece of iron at 54.9°C is cooled and releases 338 J of heat. The specific heat of iron is 0.450 J/g°C. What is the final temperature of the iron?
a 13.7°C
b 27.9°C
c 23.2°C
d 31.8°C
Solution
To solve this problem, we can use the formula for heat transfer:
q = mcΔT
where: q = heat energy (Joules) m = mass (grams) c = specific heat (Joules/gram°C) ΔT = change in temperature (°C)
We know that q = -338 J (the negative sign indicates heat loss), m = 23.7 g, and c = 0.450 J/g°C. We're solving for ΔT, which is the difference between the final temperature (Tf) and the initial temperature (Ti = 54.9°C).
Rearranging the formula to solve for ΔT gives us:
ΔT = q / (mc)
Substituting the given values:
ΔT = -338 J / (23.7 g * 0.450 J/g°C) = -31.8°C
The final temperature is then:
Tf = Ti + ΔT = 54.9°C - 31.8°C = 23.1°C
So, the closest answer is:
c) 23.2°C
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