A 6.80 kg piece of solid copper metal at an initial temperature T is placed with

Question

A 6.80 kg piece of solid copper metal at an initial temperature T is placed with 2.00 kg of ice that is initially at -16.0 C. The ice is in an insulated container of negligible mass and no heat is exchanged with the surroundings. After thermal equilibrium is reached, there is 0.60 kg of ice and 1.40 kg of liquid water.

Part A

What was the initial temperature of the piece of copper?

Express your answer to three significant figures and include the appropriate units.

A 6.80 kg piece of solid copper metal at an initial temperature T is placed with 2.00 kg of ice that is initially at -16.0 C. The ice is in an insulated container of negligible mass and no heat is exchanged with the surroundings. After thermal equilibrium is reached, there is 0.60 kg of ice and 1.40 kg of liquid water.

Part A

What was the initial temperature of the piece of copper?

Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

In the problem, some values are not given. So we make some assumptions.

Consider specific heat of ice = 2.09 kJ/kg·°C
So it takes 2.09*2*16 to raise the temperature of 2kg of ice by 16 degrees C to 0 degrees C.
= 66.88 kJ.
Again consider heat of fusion (ice to water) is 334kJ/kg.
It takes 334*1.4 kJ to melt 1.4 kg of ice at 0 degrees C to water at 0 degrees C,
= 467.6 kJ.
So 6.8 kg of copper has lost (66.88 + 467.6) kJ of heat in falling from T degrees C to 0 degrees C,
Again specific heat of copper = 0.385 kJ/kgC
So 534.48 kJ = 0.385*6.8*(T - 0)
=> 534.48 = 2.618T
=> T = 534.48/2.618 = 204.15 degrees C = Initial temperature of copper.

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