Suppose 8.50 ✕ 10^5 j of energy are transferred to 1.63 kg of ice at 0°c. the latent heat of fusion and specific heat of water are lf = 3.33 ✕ 105 j/kg and c = 4186 j (kg · °c) . hint (a) calculate the energy (in j) required to melt all the ice into liquid water. (enter your answer to at least three significant figures.) j (b) how much energy (in j) remains to raise the temperature of the liquid water? (enter your answer to at least three significant figures.) j (c) determine the final temperature of the liquid water in celsius. °c

(a) 5.43 x 10⁵ J

(b) 3.07 x 10⁵ J

(c) 45 °C

Explanation:

(a)

= Latent heat of fusion of ice to water = 3.33 x 10⁵ J/kg

m = mass of ice = 1.63 kg

= Energy required to melt the ice

Energy required to melt the ice is given as

= m

= (1.63) (3.33 x 10⁵)

= 5.43 x 10⁵ J

(b)

E = Total energy transferred = 8.50 x 10⁵ J

Q  = Amount of energy remaining to raise the temperature

Using conservation of energy

E = + Q

8.50 x 10⁵ = 5.43 x 10⁵ + Q

Q = 3.07 x 10⁵ J

(c)

T₀ = initial temperature = 0°C

T = Final temperature

m = mass of water = 1.63 kg

c = specific heat of water = 4186 J/(kg °C)

Q = Amount of energy to raise the temperature of water = 3.07 x 10⁵ J

Using the equation

Q = m c (T - T₀)

3.07 x 10⁵ = (1.63) (4186) (T - 0)

T = 45 °C

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