An insulated thermos contains 134 g of water at 70.7°c. you put in a 13.8 g ice cube at 0.00°c to form a system of ice + original water. the specific heat of liquid water is 4190 j/kg*k; and the heat of fusion of water is 333 kj/kg. what is the net entropy change of the system from then until the system reaches the final (equilibrium) temperature?

Explanation:

Given,

Let T be the final temperature of the mixture,

Therefore From the law of mixing, heat loss by the water is equal to the heat gained by the ice,

Now, We know that,

Change in the entropy,

Now, change in entropy for the ice at 0^o\ C to convert into 0^o\ C water.

Change in entropy of the water converted from ice  from to water 330.11 K water.

From the equation (1),

Change in entropy of the original water from the temperature 342.85 K to 330.11 K

From the equation (1),

Total entropy change =

Hence, the change in entropy of the system form then untill the system reaches the final temperature is 21.33 J/K