The specific heat of a certain type of metal is 0.128 J/(g·°C). What is the final temperature if 305 J of heat is added to 53.3 g of this metal initially at 20.0 °C?
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To find the final temperature, we can use the formula:
Q = m * c * ΔT
Where:
Q is the amount of heat transferred
m is the mass of the metal
c is the specific heat of the metal
ΔT is the change in temperature
In this case, we are given:
Q = 305 J (amount of heat transferred)
m = 53.3 g (mass of the metal)
c = 0.128 J/(g·°C) (specific heat of the metal)
Initial temperature, T1 = 20.0 °C
We want to find the final temperature, T2.
Rearranging the formula, we have:
ΔT = Q / (m * c)
Substituting the given values:
ΔT = 305 J / (53.3 g * 0.128 J/(g·°C))
Now we can solve for ΔT:
ΔT = 305 J / (6.8264 g·°C/J)
ΔT ≈ 44.7634 °C
To find the final temperature, we add ΔT to the initial temperature:
T2 = T1 + ΔT
T2 = 20.0 °C + 44.7634 °C
T2 ≈ 64.7634 °C
Therefore, the final temperature is approximately 64.8 °C.