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# The temperature of a piece of copper with a mass of 95.4 g increases from 25°C to 48°C when the metal absorbs 849 J of heat. What is the specific heat of copper?

##0.39"J"/("g" ""^@"C")##

A substance's tells you how much heat much be provided to increase the temperature of ##"1 g"## of that substance by ##1^@"C"##.

The equation that establishes a relationship between how much heat a substance must absorb in order to register a change in its temperature looks like this

##color(blue)(q = m * c * DeltaT)" "##, where

##q## - the amount of heat absorbed ##m## - the mass of the sample ##c## - the of the substance ##DeltaT## - the change in temperature, defined as the difference betwen the final temperature and the nitial temperature

In your case, you know that the temperature of ##"95.4-g"## sample of copper increases from ##25## to ##48^@"C"## after absorbing ##"849 J"## worth of heat.

Rearrange the equation to solve for ##c## and plug in your values

##c = q/(m * DeltaT)##

##c = "849 J"/("95.4 g" * (48-25)^@"C") = 0.38693"J"/("g" ""^@"C")##

Rounded to two , the number of sig figs you ahve for the two temperatures of the copper sample, the answer will be

##c = color(green)(0.39"J"/("g" ""^@"C"))##

It's worth noting that the result matches listed values almost perfectly

http://www.engineeringtoolbox.com/specific-heat-metals-d_152.html