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## Homework Statement

A 0.25 kg piece of ice at -30 C is warmed by an electric heater and the following graph of temperature is produced. Assume that there has been no loss of energy to the surroundings.

- Use the info on the graph to determine the power output of the heater

- Explain how long it will take to get the ice to the melting point of 0 C

- Explain how long it will take to melt completely once the ice reaches 0 C

- Create a graph like the one above for when the ice starts melting and then complete it, up to this point

## Homework Equations

Q = m

_{ice}c

_{ice}t

_{ice}

E=Q

P=Q/t

t=Q/P

## The Attempt at a Solution

First calculating the energy:

Q = mct = 0.25 kg x (2.1 x 10

^{3}J) x (-30 C - 10 C) = 10, 500 J

Then the power:

P = Q/t = 10, 500J / 150s = 70 W

Now to to find out how long it takes the ice to get to the melting point:

Q = mct = 0.25 kg x (2.1 x 10

^{3}J) x (-10 C - 0 C) = 5250 J

t = Q/P = 5250 / 70 = 75s

How long it will take the ice to melt completely once it reaches 0 C:

Q = mL

_{f}= 0.25 kg x (3.3 x 10

^{5}) = 82 500 J

t = Q/P = 82500 / 70 = 1180s approximately

Then, 1180s + 75s = 1255s

This is the approximate time it will take the ice to go from -10 C to 0 C, and then completely melt.

The graph:

Have I done everything correctly? Any confirmation and/or help is greatly appreciated.