$3\;g$ carbon are burnt in a copper calorimeter to produce $CO_2$. The calorimeter has a mass of $1,5 \;kg$ and the mass of water contained in the calorimeter equals $2\;kg$. The temperature rises from $20^oC$ to $31^oC$. Calculate the specific heat of combustion of carbon (= heat produced by the combustion of 1 gram).
The system: $3\;g$ of carbon. The surroundings: The calorimeter with its water.
Heat received by the water = $4184\cdot 2\cdot(31$ $-$ $20)$ $=$ $92000\;J$ Heat received by the calorimeter= $400\cdot 1,5\cdot(31$ $-$ $20)$ $=$ $6600\;J$
Heat received by the system = Heat lost by the calorimeter + heat lost by the water = $\color{red}-\color{black}6600$ $\color{red}-\color{black}92000$ $=$ $-98600\;J$
Specific heat of combustion of carbon (= heat lost by one gram of the system) $=$ $\frac{98600}{3}$ $\approx $ $32870\; J$