104 g of water at `30^@`C is taken in a calorimeter made of copper of mass 42 g. When a certain mass of ice at 0°C is added to it, the final steady temperature of the mixture after the ice has melted, was found to be `10^@`C. Find the mass of ice added. [Specific heat capacity of water = 4.2 J `g^(-1)""^@ C^(-1)`, Specific latent heat of fusion of ice = 336 J `g^(-1)`, Specific heat capacity of copper `= 0.4 Jg^(-1) ""^@ C^(-1)`].

Explanation

Given : `m_(w)=104g=T_(w)=30^(@)C`
`m_(c)=42g,T=10^(@)C`
`m_(i)=?`
By calorimetry,
Heat lost = Heat gained
`m_(w)S_(w)(T_(w)-T)+m_(c)S_(c)(T_(w)-T)=m_(i)alpha+m_(i)S_(w)(T-T_(i))`
`rArr(104)(4.2)(30-10)+(42)(0.4)(30-10)=m_(i)(336)+m_(i)(4.2)(10-0)`
`rArrm_(i)=((104)(4.2)(20)+(42)(0.4)(20))/((336+42))`
`m_(i)=24g`