# Heat capacity and specific heat You bring a 650 g wrench into the house from your car. The house is 21 C warmer than the car, and it takes 2.48 kJ of energy to warm the wrench by this amount. Find the heat capacity of the wrench. Find the specific heat of the metal it's made from.

We can determine the heat capacity of the wrench by looking at the information given and the units we need for the answer.  Remember that heat capacity is for a specified object and has units of J/degC.  Specific heat has J/g degC.  Heat capacity is typically used for an object of fixed mass while specific heat is used for elements/compounds that can change in mass more readily.

q = C(deltat)

where q is the heat, C is the heat capacity and deltaT is the change in temperature.  We can plug in the values we know (converting kJ to J)

2.48 x 10^3 J = C(21 degC)

C = 118 J/degC

Now that we know C, we can use the mass of the wrench to determine the specific heat by dividing by the mass

C/mass = s

where s is the specific heat.

118 J/degC / 650 g = s

s = 0.182 J/g degC

Alternatively, we could use the formula

q = m s deltaT

and solve for s (specific heat).

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