If 125 cal of heat is applied to a 60.0-g piece of copper at 23.0∘C , what will the final temperature be? The specific heat of copper is 0.0920 cal/(g⋅∘C) .
q = mass x specific heat x (Tfinal-Tinitial)
To find the final temperature, we can use the formula for heat transfer:
Q = m * c * ΔT
Where:
Q is the amount of heat transferred
m is the mass of the object
c is the specific heat capacity of the material
ΔT is the change in temperature
In this case, we want to find the final temperature, so we rearrange the formula to solve for ΔT:
ΔT = Q / (m * c)
Given:
Q = 125 cal
m = 60.0 g
c = 0.0920 cal/(g⋅∘C)
Substituting the values into the formula:
ΔT = 125 cal / (60.0 g * 0.0920 cal/(g⋅∘C))
ΔT = 2.56 ∘C
Now, to find the final temperature, we can add the change in temperature to the initial temperature:
Final temperature = Initial temperature + ΔT
Given initial temperature = 23.0 ∘C
Final temperature = 23.0 ∘C + 2.56 ∘C
Final temperature ≈ 25.56 ∘C
Therefore, the final temperature will be approximately 25.56 ∘C.
To find the final temperature of the copper, we can use the formula:
Q = mcΔT
Where:
Q is the heat energy transferred to the copper (in calories)
m is the mass of the copper (in grams)
c is the specific heat capacity of copper (in cal/(g⋅∘C))
ΔT is the change in temperature (in ∘C)
In this case, we know:
Q = 125 cal
m = 60.0 g
c = 0.0920 cal/(g⋅∘C)
ΔT = final temperature - initial temperature
First, we need to find the ΔT by rearranging the formula:
ΔT = Q / (mc)
Now, we can substitute the values:
ΔT = 125 cal / (60.0 g * 0.0920 cal/(g⋅∘C))
The grams cancel out, leaving us with:
ΔT = 125 / 0.0920 ∘C
Simplifying this calculation, we get:
ΔT ≈ 1359.78 ∘C
Finally, we can find the final temperature by adding the ΔT to the initial temperature:
Final temperature = 23.0∘C + 1359.78∘C
The final temperature will be approximately 1382.78∘C.