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. `916 J kg^(-1)K^(-1)`
B. `458 J kg^(-1)K^(-1)`
C. `1232 J kg^(-1)K^(-1)`
D. `654 J kg^(-1)K^(-1)`

Answer

A

Explanation

Subscript for unknown is ` rarr` u
Subscript for calorimeter is `rarr` c
Subscript for water is `rarr` w
`m_vS_u(100-21.5)=m_c xx S_c(21.5-8.4)+m_wS_w(21.5-8.4)`
`therefore 192 xx S_w xx 78.5 =128 xx 394 xx 13.1+240 xx 4200 xx 13.1`
`therefore S_u=(13.1(128 xx 394 +240xx4200))/(192xx78.5)`
`therefore S_u=919.94 J//kg-k`.