A sample of metal with a specific heat of .502 J/g°c is heated to 100.0°C and then placed a 50.0 g sample of water at 20.0°C. The final temperature of the system is 76.2°C. What is the mass of the metal used in process?
The mass of the metal is 459 g.
We must identify the heat transfers that are happening here.
One is the heat transferred from the metal as it cools (
The second is the heat transferred to the water as it warms (
Per the Law of Conservation of Energy, the sum of the two heat transfers must be zero.
#q_1 + q_2 = 0#
The formula for the heat absorbed by or released from a substance is
#color(blue)(bar(ul(|color(white)(a/a)q = mcΔTcolor(white)(a/a)|)))" "#
This gives us
In this problem, we have