An unknown metal of mass 192 g heated to a temperature of `100^(@)C` was immersed into a brass calorimeter of mass 128 g containing 240 g of water at a temperature of `8.4^(@)C`. Calculate the specific heat of the unknown metal if water temperature stabilizes at `21.5^(@)C`. (Specific heat of brass is `394 J kg^(-1) K^(-1)`)

Options

A. `916Jkg^(-1)K^(-1)`
B. `654Jkg^(-1)K^(-1)`
C. `1232Jkg^(-1)K^(-1)`
D. `458Jkg^(-1)K^(-1)`

Answer

A

Explanation

Heat released by the unknown metal = heat absorbed by the calorimeter and water
`rArrM_("Matel")xxS_("Metal")xx(100-21.5)=M_("brass")S_("brass")(21.5-8.4)+M_("water")S_("water")(21.5-8.4)`
`rArr192xxS_("metal")xx78.5=128xx394xx13.1+240xx4200xx13.1`
`rArrS_("metal")=919.95J//kg//k`