Question

An 8.5 g ice cube is placed into 255 g of water. Calculate the temperature change in the water upon the complete melting of the ice. Assume that all of the energy required to melt the ice comes from the water.

Answer 1

Change in temperature of water = 2.67 °C

Step-by-step explanation:

Heat gained by ice = heat lost by water

Q₁ = Q₂............... Equation 1

Where Q₁ = Latent heat of ice, Q₂ = heat lost by water

Q₁ = lm₁.................... equation 2

Q₂ = cm₂ΔT ............... Equation 3

Substituting equation 2 and 3 into equation 1

lm₁ = cm₂ΔT............... Equation 4

Making ΔT the subject of formula in equation 4

ΔT = lm₁/cm₂............. Equation 5

Where ΔT = change in temperature of water, l = specific latent heat of ice, m₁ = mass of ice, c= specific heat capacity of water, m₂ = mass of water.

Given: m₁ = 8.5 g = 0.0085 kg, m₂ = 255 g = 0.255 kg.

Constant: l = 336000 J/kg, c = 4200 J/kg.K

Substituting these values into equation 5

ΔT = (336000×0.0085)/(0.255×4200)

ΔT = 2856/1071

ΔT = 2.67 °C

Change in temperature of water = 2.67 °C