Answer :
Answer:
The specific heat capacity of the material (Cp) is
Cp= 0,1378 J/gr K
Explanation:
Assuming
1) the calorimeter is completely insulated ( has no heat losses)
[tex]Q_{min}+ Q_{water} +Q_{cal} = Q_{out} =0\\[/tex]
2) the system reaches equilibrium ( the mineral, water and calorimeter has the same final temperature).
3) The specific heat of water is 4,186 J/gK and remains constant
Therefore
[tex]m_{min}c_{min}(T_{equil}- T_{min})+ m_{w}c_{w}(T_{equil}- T_{cal}) +m_{cal}c_{cal}(T_{equil}- T_{cal}) =0\\\\m_{min}c_{min}(T_{equil}- T_{min})+(m_{w}c_{w} +m_{cal}c_{cal})(T_{equil}- T_{cal}) =0\\\\\\m_{min}c_{min}(T_{equil}- T_{min})= - (m_{w}c_{w} +m_{cal}c_{cal})(T_{equil}- T_{cal})\\\\c_{min}= - (m_{w}c_{w} +m_{cal}c_{cal})(T_{equil}- T_{cal})/[m_{min}(T_{equil}- T_{min})]\\\\\\c_{min}= - (72,4gr*4,186 J/gK +15,7 J/K )(32,4 C- 23,6 C)/[307 gr *(32,4 C- 98,7 C]\\ = 0,1378 J/gK[/tex]