How much heat must be added to 0.55 kg of aluminum to change it from a solid at

Question

How much heat must be added to 0.55 kg of aluminum to change it from a solid at 110degree C to a liquid at 660degree C (its melting point)? The latent heat of fusion for aluminum is 4.0 times 10^5 J/kg. J A thermos contains 175 cm^3 of coffee at 85degree C. To cool the coffee, you drop two 15-g ice cubes into the thermos. The ice cubes are initially at 0degree C and melt completely. What is the final temperature of the coffee? Treat the coffee as if it were water. (See Table 12.2 and Table 12.3 for appropriate constants.) degreeC An unknown material has a normal melting/freezing point of -27.5degree C, and the liquid phase has a specific heat capacity of 160 J/(kg middot Cdegree). One-tenth of a kilogram of the solid

Explanation / Answer

8.

First, we need to calculate the heat energy needed to raise the temperature of aluminium to 660 degrees using the formula Q= mcT where m is the mass of aluminium, c is the specific heat capacity of aluminium and T is the change in temperature
Q= (0.55)(910)(660-110)
= 2.75275x10^5J

Then, we need to calculate the heat energy needed to convert the aluminium from solid phase to liquid phase using the formula Q= mL where L is the latent heat of fusion of aluminium
Q= mL
= (0.55)(4.0105)
= 2.2 * 10^5 J

Thus, the total amount of heat energy needed= (2.75275x10^5)+2.2 * 10^5
= 495275 J

9.

msT = m's'T + mL
This being that you have a chage in state (the ice turns into water)
m= 0.175Kg
m'= 0.030 Kg
s= 4186 J / Kg * C (constant for both since the coffee is treated as water)
T initial of the coffee = 85 C
T initial of ice = 0 C
L= 33.5 x 10 ^4 J/Kg (Latent heat of fusion of water since ice is turning into liquid)
Tf = final temperature

so

Always put the highest temperature first so you dont have to worry if exothermic or endothermic
(.175 Kg)(4186 J/Kg*C)(85 C - Tf) = (0.030Kg)((4186 J/Kg*C)(Tf - 0 C) + (0.030Kg)(33.5x10^4 J/Kg)

simplify and distribute
62266.75 - 732.55 Tf = 125.58 Tf - 0 + 10050

Solve for Tf

Tf = 60.849

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