Assume a 5 gm of frozen ice at 0degree C is mixed with 5 gm

Assume a 5 gm of frozen ice at 0degree C is mixed with 5 gm of culture mammalian cells at 25degree C in an isolated system during an in-vitro experimentation. Subsequently 1 gm of steam was further exposed to the above mixture in the experiment. Determine the total mass and final temperature of the product of the mixture at thermodynamic equilibrium taking approximation of the cytoplasmic cell composition to water.

Solution

mass of ice m = 5 g

Initial temprature of ice t = 0 ^o C

mass of cell m \' = 5 g

Initial temprature of cell t \' = 25 ^o C

Mass of steam m \" = 1 g

Latent heat of fusion L = 334 J / g

Specific heat of water C = 4.186 J / g ^o C

Latent heat of vaporisation of water L \' = 2256 J / g

Total mass of the mixture M = m+ m \' + m \"

                                         = 11 g

Heat lost by steam = heat gain by cell + heat gain by ice

m\"L\' +m\" C (100-T ) = m\'C(T - t \' ) + mL + mCT

(1 x2256) +[(1 x 4.186 (100-T)]= [5x4.186 x(T -25) ]+ (5 x 334) +(5 x4.186 T)

2256 + 418.6 -4.186 T = - 523.25 + 20.93 T + 1670 +20.93 T

          46.046 T = 2256+418.6+523.25-1670

                                  = 1527.85

                                T = 33.18 ^o C