Question

A 9.0×10⁻²-kg ice cube at 0.0 ∘C is dropped into a Styrofoam cup holding 0.35 kgkg of water at 10 ∘C∘

A. Find the final temperature of the system. Assume the cup and the surroundings can be ignored.

B.Find the amount of ice (if any) remaining.

C. Find the initial temperature of the water that would be enough to just barely melt all of the ice.

Express your answer using two significant figures.

Answer 1

Latent heat of fusion of ice Lf= 3.34* (10^5) J/Kg

Amount of heat required for melting the given mass of ice, Q1 = m* Lf = 9.0* (10^-2)* 3.34* (10^5) = 30.06 * (10^3) = 30060 J

Amount of heat, that can be liberated when the given amount of water is lowered to 0°C , Q2 = M* C* ∆T = 0.35* 4200* 10 = 14700 J [C - specific heat of water)

A) Heat available from cooling of water is less than heat required for melting of ice.

So final temperature of the system will be 0°C itself.

B) Amount ice melted using heat available from cooling of water, m1 = Q2/ Lf = 14700/ (3.34* (10^5)) = 4.4* (10^-2) Kg

So amount of ice reaming = m-m1 = 9.0 * (10^-2) - 4.4* (10^-2) = 4.6 * (10^-2) Kg

C) for all the ice to melt, temperature of water must be T

Then Q2 = M*C* T

Total heat required,Q1 = 30060 J

T= 30060/M* C= 30060/(0.35* 4200) = 20.45 °C