kilojoules to heat 165 g of copper from 28 ∘C to 185 ∘C.

Side note question what is (T-final-Tinitial) means exactly?

Yes. Exactly. Well done.

To calculate the amount of heat required to heat a substance, you can use the equation:

Q = mcΔT

Where:
Q is the amount of heat required (in joules),
m is the mass of the substance (in grams),
c is the specific heat capacity of the substance (in joules/gram⋅degree Celsius), and
ΔT is the change in temperature (in degrees Celsius).

Now let's calculate the amount of heat required to heat 165 g of copper from 28 °C to 185 °C:

1. The first step is to determine the specific heat capacity of copper. The specific heat capacity of copper is approximately 0.39 J/g⋅°C. This means that 0.39 joules of heat are required to raise the temperature of 1 gram of copper by 1 degree Celsius.

2. Next, calculate the change in temperature (ΔT):
ΔT = T final - T initial
= 185 °C - 28 °C
= 157 °C

3. Now we can plug the values into the equation:
Q = (mass) x (specific heat capacity) x (change in temperature)
= 165 g x 0.39 J/g⋅°C x 157 °C

Calculate the value using a calculator:
Q ≈ 9690.45 J

To convert joules to kilojoules, divide the value by 1000:
Q ≈ 9.69 kJ

Therefore, approximately 9.69 kilojoules of heat are required to heat 165 g of copper from 28 °C to 185 °C.

Now, regarding your side note question, "T-final" refers to the final temperature of the substance, while "T-initial" refers to the initial temperature of the substance. The expression "(T-final - T-initial)" represents the change in temperature of the substance.

q = mass Cu x specific heat Cu x (Tfinal - Tinitial)

q = 165 x specific heat Cu (you look it up) x (Tf - Ti) = ?
Post your work if you get stuck.
Note: I have no idea what (T-final - Tinitial) means, either exactly or otherwise. I've answered several heat question today and I thought perhaps I made a typo; however, I looked, I thought, at all of my responses and I didn't see a typo. If you are the one that made a typo and you meant to ask about the meaning of (Tfinal - Tintial), here it is.
Tinitial is the initial temperataure (starting temperature in the problem) while Tfinal is the final temperature (ending temperature in the problem). In this Cu problem, Tinitial or Ti is 28 C and Tfinal or Tf is 185 C. Hope that clears things up.

So here's my problem to that question..

(165g) (4.184) (185-28) = 108386.52
and then divide that by 1000 so it would be like this.. 108386.52/1000 and that equals to 108.38652 and then its asking for 3 SFs wouldn't that be 108 KJ?