Question

A chunk of ice, initially at -10◦C, is placed in 3 kg of water at 20◦C. (The ice and water only exchange heat with each other.) What mass of ice is needed to produce (liquid) water at 0 ◦C?

Answer 1

let mass of ice= m kg

heat absorbed by ice to change from ice at -10 deg into water at 0 deg= m L + m C (change in tempearture

whre L= 3.33 x 10⁵J/kg. and is the altent heat of fusion of ice and c= sepcific heat of ice= 2090j/kg c

Heat absorbed by ice=Qa=m ( 3.33 x 10⁵ ) + m (2090)(0-(-10))

Qa= 3.33 x 10⁵ m +20900 m

Qa=3.539x10⁵ m

heat lost by water= m c (change in temp)

Ql= 3 (4180) (0-20)

Ql=-2.508x10⁵

now total heat =0

QL+ Qa=0

-2.508x10⁵ +3.539x10⁵ m =0

3.539x10⁵ m = 2.508 x10⁵

m= (2.508x10⁵)/(3.539x10⁵)

m=0.71 kg