Question

1 kg of ice at 0 degree C is mixed with 1 kg of water at 80 degree C the final temperature of the mixture is​

Answer 1

Given info : 1 kg of Ice at 0°C is mixed with 1 kg of water at 80° C.

To find : The final temperature of the mixture is...

solution : we know, heat flows from higher temperature to lower temperature.

so, water released an amount of heat and ice gained that heat.

heat gained by ice to melt completely ,h = mLf

= 1kg × 80 kcal/kg [ we know latent heat of fusion is 80 kcal/kg ]

= 80 kcal

and heat lost by water to decrease it temperature to 0° , H = mS∆T

= 1kg × 4.2 kcal/kg/°C × 80°C

= 80 × 4.2

= 336 kcal

we see h < H

so, ice melts and then increase its temperature upto t°C

h + mSt = ms(T - t)

⇒80 kcal + 1 kg × 4.2 kcal/kg/°C × t = 1kg × 4.2 kcal/kg/°C × (80 - t)

⇒80 = 4.2 × (80 - 2t)

⇒19 = 80 - 2t

⇒2t = 80 - 19 = 61

⇒t = 30.5°C

Therefore the final temperature of the mixture is 30.5°C