Basic Heat energy Transfer

**Strings (S _{i}P_{j}A_{jk}) = S_{7}P_{5}A_{51} Base Sequence = 12735 String Sequence = 12735 - 5 - 51**

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A piece of Aluminum of mass 3.90 g at temperature 99.3^{o}C is immersed into a 10.0 cm^{3} of water at 22.6 ^{o}C (figure 7.2). Determine the final temperature of the system.

**The strings**:
S_{7}P_{5}A_{51} (Change - Physical).
**The math**:

Pj Problem of Interest is of type *Change* (physical).

Assumption: system is insulated

Let q = heat gained or lost; m = mass in grams; C_{p} = specific heat;

ΔT = change in temperature = T_{final} - T_{initial} (when heat is gained).

ΔT = change in temperature = T_{initial} - T_{final} (when heat is lost).

By the law of conservation of energy:

q = m(ΔT)C_{p} --------(1)

q_{lost} = q_{gained} -------(2)

Now mass of water = Density x Volume = 1 x 10 g/cm_{3}.

So from equation (2):

(3.90)(99.3 - T_{final})(0.903) = (10)(22.6 - T_{final})(4.18)

So, final temperature of system, T_{final} = 28.6^{o}C.

The *point* **.** is a mathematical abstraction. It has negligible size and a great sense of position. Consequently, it is front and center in abstract existential reasoning.

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