Heat and Thermodynamics 1 Question 6

6. Ice at 20C is added to 50g of water at 40C. When the temperature of the mixture reaches 0C, it is found that 20g of ice is still unmelted. The amount of ice added to the water was close to (Take, specific heat of water =4.2J/g/C specific heat of ice =2.1J/g/C and heat of fusion of water at 0C=334J/g)(2019 Main, 11 Jan I)

(a) 40g

(b) 50g

(c) 60g

(d) 100g

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Solution:

  1. Let amount of ice be ’ xgm.

According to the principle of calorimeter,

heat lost by water = heat gained by ice

Here, heat lost by water

ΔQ=mswater ΔT

Substituting the given values, we get

ΔQ=50×4.2×40

Heat gained by ice,

ΔQ=xsice ΔT+(x20)L=x×2.1×20+(x20)×334=20x×2.1+334x668020x×2.1+334x6680=50×4.2×4042x+334x6680=8400376x=15080 or x=40.10gx40g



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