Well, if we're talking about melting ice at -45°C, I'd say it's going to take a whole lot of heat! In fact, it's going to be colder than a penguin's freezer in there! But let's get down to the nitty-gritty. The specific heat capacity of ice is around 2.09 J/g°C, and the heat of fusion for ice is approximately 334 J/g.
First, we need to warm up the ice from -45°C to 0°C. That'll take some serious effort, but using the specific heat capacity, we can calculate the heat required for that.
Q1 = m * c * ΔT
Q1 = 110g * 2.09 J/g°C * (0°C - -45°C)
Q1 = 110g * 2.09 J/g°C * 45°C
Q1 = 10395 J
So we need 10395 J to warm up the ice to 0°C.
Next, we need to melt the ice at 0°C into water at 0°C. To do that, we use the heat of fusion.
Q2 = m * ΔHf
Q2 = 110g * 334 J/g
Q2 = 36740 J
We need 36740 J to melt the ice at 0°C.
Now we add the two amounts of heat together to get the total amount of heat required:
Total heat = Q1 + Q2
Total heat = 10395 J + 36740 J
Total heat = 47135 J
So, it'll take approximately 47135 J of heat to melt 110g of ice at -45°C. That's enough heat to make even the most frigid heart melt!