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Water Fall - Potential Energy To Thermal Energy

The water at the bottom of a water fall is warmer than the water at the top of the water fall because of the conversion of potential energy into thermal energy. Consider a water fall that is 160 ft high. How much warmer is 1 kg of water at the bottom of the water fall than at the top of the water fall if the acceleration due to gravity is 9.81 m/sec^{2}?

**The strings**:

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

Pj Problem of Interest (PPI) is of the type *change*. Problems of temperature change are in general *change problems*.

160 ft = 0.3048(160) meters = 48.77 meters.

1 kg of water at top of water fall has mgh potential energy = 1 x 9.81 x 48.77 = 478 Joules.

So, potential energy converted to thermal energy = 478 Joules.

Energy required to raise 1 kg of water by 1^{0}C = 4184 J (specific heat of water = 4.184 J).

So, Increase in temperature of water at bottom of water fall = 478/4184 = 0.114^{0}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

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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

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Boolean Algebra - Logic Functions

Ordinary Differential Equations (ODEs)

Infinite Sequences And Series

Introduction To Group Theory

Advanced Calculus - Partial Derivatives

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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

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Molecular Orbital Theory

More Pj Problem Strings