# An ancient copper coin was found to absorb 545.8 J of heat when the temperature increases 31.4 C°. The specific heat of copper is 0.387 J/g°C. What is the mass of the copper coin?

Jun 10, 2016

The mass of the copper coin is 44.9 g.

The formula for the heat absorbed by a substance is

color(blue)(|bar(ul(color(white)(a/a) q = mcΔT color(white)(a/a)|)))" "

where

$q$ is the quantity of heat

$m$ is the mass of the substance

$c$ is the specific heat capacity of the material

ΔT is the temperature change

You can rearrange the formula to calculate the specific heat capacity:

m = q/(cΔT)

m = (545.8 color(red)(cancel(color(black)("J"))))/(0.387 color(red)(cancel(color(black)("J·°C"^"-1")))"g"^"-1" × 31.40 color(red)(cancel(color(black)("°C")))) = "44.9 g"

Wouldn't it have been easier to weigh the coin on a balance?