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 57.2 g of this metal initially at 20.0 °C?
q = mass x specific heat x (Tfinal-Tinitial)
Substitute into the equation and solve for Tfinal.
To find the final temperature, we can use the formula:
q = m * c * ∆T
where:
q = heat absorbed or released by the substance
m = mass of the substance
c = specific heat capacity of the substance
∆T = change in temperature
In this case, the heat absorbed by the metal is given as 305 J. The mass of the metal is 57.2 g. The specific heat capacity of the metal is 0.128 J/(g·°C). The metal is initially at 20.0 °C, and we want to find the final temperature.
Rearranging the formula, we have:
∆T = q / (m * c)
Substituting the given values:
∆T = 305 J / (57.2 g * 0.128 J/(g·°C))
Simplifying the expression within the parentheses:
∆T = 305 J / (7.3344 J/°C)
Dividing to find ∆T:
∆T ≈ 41.61 °C
To find the final temperature, we add ∆T to the initial temperature:
Final temperature = Initial temperature + ∆T
Final temperature ≈ 20.0 °C + 41.61 °C
Final temperature ≈ 61.61 °C
Therefore, the final temperature is approximately 61.61 °C when 305 J of heat is added to 57.2 g of this metal initially at 20.0 °C.