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QUESTION

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