Question

A chunk of ice of mass m₁ = 100 g at a temperature t₁ = 0 °C was placed in a calorimeter in which water of mass m₂  = 100 g was at a temperature t₂. Assuming the heat capacity of the calorimeter to be negligible, find the entropy increment of the system by the moment the thermal equilibrium is reached. Consider two cases: 

(a) t₂ = 60°C; 

(b) t₂ =  94°C.

Answer 1

(a) Here t₂ = 60°C. Suppose the final temperature is t°C. Then heat lost by water = m₂ c (t₂ -1) 

heat gained by ice = m₁ q_m + m₁ c (t - t₁ ), if all ice melts In this case m₁ q_m = m₂ x 4.18 (60 - t)  for m₁ = m₂ 

So the final temperature will be 0°C and only some ice will melt.

(b) If m₂ct₂>m₁q_m  then all ice will melt as one can check and the final temperature can be obtained like this