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Basic Heat Energy Transfer

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.

Math

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.

Derivation Of The Area Of A Circle, A Sector Of A Circle And A Circular Ring

Derivation Of The Area Of A Trapezoid, A Rectangle And A Triangle

Derivation Of The Area Of An Ellipse

Derivation Of Volume Of A Cylinder

Derivation Of Volume Of A Sphere

Derivation Of Volume Of A Cone

Derivation Of Volume Of A Torus

Derivation Of Volume Of A Paraboloid

Volume Obtained By Revolving The Curve y = x^{2} About The X Axis

Single Variable Functions

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Equation Of The Ascent Path Of An Airplane

Calculating Capacity Of A Video Adapter Board Memory

Probability Density Functions

Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

Advanced Calculus - General Charateristics Of Partial Differential Equations

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Advanced Calculus - Solving PDEs By The Method Of Separation Of Variables

Advanced Calculus - Fourier Series

Advanced Calculus - Multiple Integrals

Production Schedule That Maximizes Profit Given Constraint Equation

Separation Of Variables As Solution Method For Homogeneous Heat Flow Equation

Newton And Fourier Cooling Laws Applied To Heat Flow Boundary Conditions

Fourier Series

Derivation Of Heat Equation For A One-Dimensional Heat Flow

Homogenizing-Non-Homogeneous-Time-Varying-IBVP-Boundary-Condition

The Universe is composed of *matter* and *radiant energy*. *Matter* is any kind of *mass-energy* that moves with velocities less than the velocity of light. *Radiant energy* is any kind of *mass-energy* that moves with the velocity of light.

Periodic Table

Composition And Structure Of Matter

How Matter Gets Composed

How Matter Gets Composed (2)

Molecular Structure Of Matter

Molecular Shapes: Bond Length, Bond Angle

Molecular Shapes: Valence Shell Electron Pair Repulsion

Molecular Shapes: Orbital Hybridization

Molecular Shapes: Sigma Bonds Pi Bonds

Molecular Shapes: Non ABn Molecules

Molecular Orbital Theory

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