Question

An ice cube of mass 11.4 g and initial temperature -6.0°C is held in your hand such that the water resulting from the melted ice reaches the temperature of your hand, 36.2°C. In order to accomplish this, how much heat (in kJ) must be absorbed by the ice cube and resulting water? Assume that all the water remains in your hand. Hint: Tables 14.1 and 14.2 in your textbook will be useful here.

Answer 1

First ice was at an initial temperature, . From the heat absorbed from the hand, it reach to 0^oC. Heat absorbed during this process,

where

Note: Degree celsius+273.15=Kelvin Here is difference, hence it is same value for celsius and kelvin

C_i is specific heat capacity of ice =2093 J/K/kg

Hence heat absorbed,

Next ice melts into water. Then the energy required by the ice cube for melting is,

where m is the mass of ice cube and L_f is latent heat of fusion. The L_f of the ice at 0^oC is 334 J/gm.

Hence the heat for melting is,

Now once the ice melts completely to ice, temperature of water started increases and reach upto 36.2 ^oC. The heat absorbed during this is,

where

C_w =4182 J/K/Kg

Hence total heat absorbed,