4 kg of ice at`-20^(@)C` is mixed with 10 kg of water at `20^(@)C` in an insulating vessel having a negligible heat capacity. Calculate the final mass of water remaining in the container, Given : Specific heat capacities of water and ice are `4.184 kJ K^(-1) kg^(-1) and 2.092 kJ K^(-1) kg^(-1),` respectively. Molar enthalpy of fusion of ice is `334.7 kJ kg ^(-1).`

Options

A. 8 kg
B. 10 kg
C. 12 kg
D. 14 kg

Answer

C

Explanation

The conservation of heat gives `m _(1) C _(1) (20 K) + m _(1) Delta _(fis) H - m _(w) C _(w) (20 k) = 0`
`(4kg) ( 2. 0 92kJ K ^(-1) kg ^(-1)) (20 K ) + m _(1) ( 334. 7 kJ mol ^(-1)) - (1 - kg ) ( 4.184 kJK ^(-1) kg ^(-1)) ( 20 K) = 0`
This gives
`m = [((10)(4.184) (20)- (4) (2. 0 92) (20))/(33.47)]kg = ((836.8- 167.36)/(334. 7)) kg = ((669 . 44)/(334. 7)) kg = 2.0 kg `
Hence, mass of water in the container is `m = (10 kg) + (2kg) = 12 kg.`