Question

If we want to only use frozen water (ice) and room temperature water (room temperature water of four times the mass of the ice), write out the various forms of heat transfer that will occur between frozen water and room temperature water, when the come into contact.

Hint: There will be one term of heat transfer from the room temperature water, and three terms of heat transfer in the ice/cold water.

Answer 1

Let water be at room temperature +t deg C

ice initially has some negative temperature. ( - x deg C )

this ice absorbs heat from water at room temperature and comes from - x deg C  to 0 deg Celcius. ( 1st term)

= M(ice) *Specific heat of ice * x

then at 0 deg C , the entire ice melts by absorbing further heat from water at room temperature. ( 2nd term)

= M(ice) x L , where L= latent heat of Ice

After entire ice has melted and it has become water at 0 deg C , any further heat gain from water at romm temperature will raise water at 0 deg C to + y degC , which will be common equilibrium temperature of water initially room temperature as well as water generated by melted ice.

Heat absorbed = M(ice) *Specific Heat of water * y

Heat lost by water at room temperature = M(water) x specific heat of water x ( t - y )

M(water) x specific heat of water x ( t - y ). = M(ice) *Specific heat of ice * x + M(ice) x L+M(ice) *Specific Heat of water * y

So in all water at +t deg C will come down to +y deg C.

Ice initially at - x deg C will turn to water at + y deg C