Question

1g water at 100° C is passed in to an insulating vessel having 1g of ice at 0° C. Find the equilibrium
temperature of the mixture, neglecting heat capacity of the vessel.
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Answer 1

1g water at 100°C is passed into an insulating vessel having 1g of ice at 0°C. here neglecting heat capacity of the vessel.

To find : The equilibrium temperature of the mixture.

solution : water is at 100°C and ice is at 0°C so heat flows from water to ice.

let equilibrium temperature is T

heat lost by water, H₁ = mS∆T

= 1g × 4.2 J/g/°C × (100°C - T)

= 4.2(100 - T)

heat gained by ice to melt it, h₂ = mLf

= 1g × 336 J/g = 336 J

now heat required to increase the temperature of molten ice, h₃ = mS∆T

= 1g × 4.2 J/g × (T - 0°C)

= 4.2T

from Calorimetry,

heat lost = heat gained

⇒H₁ = h₂ + h₃

⇒4.2(100 - T) = 336 + 4.2T

⇒420 - 4.2T = 336 + 4.2T

⇒420 - 336 = 8.4T

⇒84 = 8.4T

⇒T = 10°C

Therefore the equilibrium temperature will be 10°C