Assume that 98 g of ice (0 degree C) is added to 380 g of water initially at 69

Question

Assume that 98 g of ice (0 degree C) is added to 380 g of water initially at 69 degree C. The water is inside an aluminum cup of mass 35 g. The cup is inside a perfectly insulating calorimetric container that prevents heat flow from the outside environment. Find the final temperature of the water after equilibrium is reached. Specific heat of water: 4.19 kJ/(kg Times K) or 1.00 cal/(g Times K) Specific heat of aluminum: 922 J/(kg Times K) or 0.22 cal/(g Times K) Latent heat of fusion for water: 334 kJ/kg or 79.7 cal/g Latent heat of vaporization for w-ater: 2260 kJ/kg or 539 cal/g

Explanation / Answer

Here ,

let the final temperature of the water is Tf

mass of ice , mi = 98 gm

mass of water , mw = 380 gm

initial temperature , Ti = 69 degree C

mass of aluminium , mA = 35 gm

heat lost by water and aluminium = heat gain by ice

380 * 4.186 * (69 - Tf) + 35 * 0.922 * (69 - Tf) = 98 * (334 + 4.186 * (Tf - 0))

solving for Tf

Tf = 38.9 degree C

the final temperature at equilibrium is 38.9 degree C

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