Final answer:
To find the final temperature of the metal when 305 J of heat is added to 71.6 g of it initially at 20.0 °C, we use the specific heat equation. The change in temperature (ΔT) is calculated to be 33.2 °C, resulting in a final temperature of 53.2 °C.
Step-by-step explanation:
The question involves the concept of specific heat capacity in physics, which is the amount of heat needed to raise the temperature of one gram of a substance by one degree Celsius. The specific heat capacity formula is given by:
q = m × c × ΔT
where q is the amount of heat added (in joules), m is the mass of the substance (in grams), c is the specific heat capacity (in J/(g°C)), and ΔT is the change in temperature (in °C).
Given that the specific heat of the metal is 0.128 J/(g°C), the mass of the metal is 71.6 g, the initial temperature is 20.0 °C, and the heat added is 305 J, we can rearrange the above formula to solve for the final temperature:
ΔT = °C = q / (m × c)
Plugging in the values gives us ΔT = 305 J / (71.6 g × 0.128 J/(g°C))
ΔT = 33.2 °C (rounded to one decimal place)
To find the final temperature, we add the change in temperature to the initial temperature:
T_final = T_initial + ΔT = 20.0 °C + 33.2 °C
T_final = 53.2 °C