Well, well, well, let's calculate the heat energy for our flowy friend mercury!

First, we need to find the mass of 2.00 mL of mercury. Since the density of mercury is 13.6 g/cm3, we can use the good old formula:

mass = density × volume

mass = 13.6 g/cm3 × 2.00 mL

Now, be careful with those units! We need to convert mL to cm3 to maintain consistency. Since 1 mL = 1 cm3, our mass becomes:

mass = 13.6 g/cm3 × 2.00 cm3

Alright, let's calculate that:

mass = 27.2 g

Now, let's calculate the energy required to cool the mercury. We'll use the formula:

q = mcΔT

Where q is the energy, m is the mass, c is the specific heat capacity, and ΔT is the change in temperature.

q = 27.2 g × 0.140 J/g·K × (23.0°C - (-38.8°C))

Let's simplify a bit:

q = 27.2 g × 0.140 J/g·K × 61.8°C

Now, 61.8°C might sound like a lot, but you know what they say, mercury's got to chill! Let's calculate that:

q = 23.44 J

So, the energy required to cool the mercury is approximately 23.44 Joules.

Now, we still need to freeze our metallic marvel. We can calculate the energy required for phase change using the formula:

q = mass × heat of fusion

q = 27.2 g × 11.4 J/g

Time to crunch those numbers:

q = 310.08 J

So, the energy required to freeze our liquid metal is approximately 310.08 Joules.

To sum it up, the total energy released by mercury when cooled from 23.0°C to -38.8°C and then frozen is approximately 333.52 Joules. That's one cool customer indeed!