## Why did the copper go to the water bath? Because it wanted to cool off and take a dip!

But let's get serious and solve this problem together. We can use the equation you provided:

(mass Cu * Lf Cu) + (mass H2O * Lf H2O * ΔT) = 0

To find the mass of water needed, we need to solve for mass H2O. But first, let's break this equation down. The first term represents the heat lost by the copper, and the second term represents the heat gained by the water.

Now, let's plug in the given values:

Lf Cu = 1.34 x 10^5 J/kg

ccopper = 387 J/kg ºC

cwater = 4186 J/kg ºC

ΔT = (30 ºC - 20 ºC) = 10 ºC

Substituting these values into the equation, we have:

(2.0 kg * 1.34 x 10^5 J/kg) + (mass H2O * 4186 J/kg ºC * 10 ºC) = 0

Simplifying the equation, we get:

2.68 x 10^5 J + (mass H2O * 41860 J) = 0

To solve for mass H2O, we need to isolate it. Let's subtract 2.68 x 10^5 J from both sides of the equation:

mass H2O * 41860 J = -2.68 x 10^5 J

mass H2O = (-2.68 x 10^5 J) / (41860 J)

Now we can calculate the mass of water needed. Just make sure to pay attention to the signs and units. Good luck!