Question

4:162 4:16 latencom login.physicscurriculum.com Calorimetry ** A 53.0 g ice cube, initially at 0.00 °C, is dropped into a Styrofoam cup containing 373 g of water, initially at 29.0 °C. What is the final temperature of the water, if no heat is transferred to the Styrofoam or the surroundings? The latent heat of melting for ice is 79.7 cal/g. Part 1 + Give the equation used for finding the heat required to melt an object of mass m and with a latent heat of melting of L. Q= Part 2 What is the final temperature of the water, if no heat is transferred to the Styrofoam or the surroundings? degrees Celsius

Answer 1

mass of the ice m₁ = 53 g, its initial temperature t₁ = 0 ⁰C
mass of the water in the cup m₂ = 327g, its initial temperature t₂ = 20.8 ⁰C
the temprature of mixture t =?
ice gains heat in two steps

1) for melting of ice Q₁= m₁L = 53*79.7 = 4224.1 cal

2) to rice the ice water temp to final Q₂ = m₁*s*dt₁
Q₂ = 53*1*(t-0) = 53t

Total gain = Q₁+Q₂ = 4224.1 + 53t

Water in the cup losses heat Q₃ = m₂*s*dt₂ = 373*1*(29 - t) = 10817 - 373t

no heat transmitted to surroundings so Q₁+Q₂ = Q₃

Q = m₁L +  m₁*s*dt₁   <<<<<< answer part A

4224.1 + 53t = 10817 - 373t

t = 15.48 ⁰C is the final temperature <<<<<<<answer part B

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