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

Explanation

The conservation of heat gives `m _(1)C _(1)(20 k) + m _(1) Delta _(fas) H = m _(w) C _(w) (20 K) = 0`
`( 4kg ) ( 2. 0 92kJ K ^(-1)kg ^(-1)) ( 20 K) + m _(1) ( 334. 7 kJ kg ^(-1)) - (10 kg) (4.18 kJ K ^(-1) kg ^(-1)) (20 K) = 0`
This gives
`m . = [ ((10) ( 4.184 ) (20) - (4) (2.092) (20))/( 334.7)] kg = ((836.8 - 167.36)/( 334. 7)) kg = ((669.44)/(334.7)) kg = 2. 0 kg `
Hence, mass of water in the containeer is `m = ( 10 kg) + (2kg ) = 12 kg. `