This problem is providing us with the mass (70 g), absorbed heat (96 J) and initial and final temperatures (293 K and 313 K, respectively) so the specific heat of the material is required and found to be 0.0686 J/(g*K) as shown below:
In chemistry, we can go over calorimetry by writing the following relationship among heat, mass, specific heat and temperature change:
[tex]Q=mC(T_f-T_i)[/tex]
Thus, one can get the specific heat by solving for C in the previous equation:
[tex]C=\frac{Q}{m(T_f-T_i)}[/tex]
Hence, we can plug in the given data to obtain:
[tex]C=\frac{96J}{70g(313K-293K)}\\ \\C=0.0686\frac{J}{g*K}[/tex]
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