Here's what I got.
A substance's specific heat tells you how much heata is needed to increase the temperature of
The equation that establishes a relationship between heat absorbed and increase in temperature looks like this
#color(blue)(q = m * c * DeltaT)" "#, where
In your case, you know that
- your metal sample has a mass of
- the temperature of the sample increases from
#25.00^@"C"#to #32.00^@"C"#after adding #"178.1 J"#worth of heat to it
So, plug in your values and solve for
#c = q/(m * DeltaT)#
#c = "178.1 J"/("15.0 g" * (32.00 - 25.00)^@"C") = color(green)(1.70"J"/("g" ""^@"C"))#
SIDE NOTE This is a very high value to get for the specific heat of a metal, so make sure that you double-check the values you were given for heat absorbed, mass, and temperature change.
The way I see it, either the mass of the sample or the temperature change are too small, or the amount of heat absorbed is too high.