Equilibrium Temperature Of Water Mixed With Ice

Equilibrium Temperature Of Water Mixed With Ice
TECTechnics Classroom TECTechnics Overview

40 grams of ice at 0^oC is mixed with 100 grams of water at 60^oC.
Determine the final temperature of the water after equilibrium has been established.
Heat of fusion of water (H₂O) = 80 cal/gram
Heat capacity/Specific Heat of water = 1 cal/gram degrees C.

The strings:

S₇P₅A₅₁ (change - physical change)

The math:
Pj Problem of Interest is of type change. The melting of the ice in the water changed the water temperature from 60^oC to an equilibrium temperature. It is this final temperature due to temperature change that is of interest eventhough heat energy is operative.

Heat Of Vaporization: the quantity of heat required to vaporize 1 gram of a liquid substance at its boiling point at constant temperature.
Heat Of Fusion: the quantity of heat required to liquefy 1 gram of a solid substance at its melting point at constant temperature.
Specific Heat: number of calories required to raise the temperature of 1 gram of liquid by 1 degree.

Heat accounting:
(1) Ice needs heat to melt
(2) The cold water from the melted ice needs heat to warm up to the equilibrium temperature.
(3) The sum of the heat from (1) and (2) is total heat absorbed.
(4) The water at 60^oC is the source of the heat needed for (3). Therefore it will loose that amount of heat.

Heat required to melt 40 grams of ice = 40 x 80 = 3200 cal.
Amount of heat absorbed by melted water before attaining final temperature, t (equilibrium temperature):
= 40 x specific heat of water x t = 40 x 1 x t = 40t.
So, total heat absorbed = 3200 + 40t.

Temperature change of water from 60⁰C to t^oC = 60 - t
So, amount of heat lost by water at 60^oC
= weight of water x specific heat of water x temperature change
= 100 x 1 x (60 - t) = 100(60 - t) = 6000 -100t

Heat absorbed = heat lost
So, 3200 + 40t = 6000 - 100t
So, 2800 = 140t
So, t = 20^oC.
So, final temperature (equilibrium temperature) = 20^oC.
Temperature of water dropped by 40^oC.

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 = x² About The X Axis
Single Variable Functions
Absolute Value Functions
Conics
Real Numbers
Vector Spaces
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
Advanced Calculus - Jacobians
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
More Pj Problem Strings

What is Time?
St Augustine On Time
Bergson On Time
Heidegger On Time
Kant On Time
Sagay On Time

What is Space?
Newton On Space
Space Governance
Leaders
Imperfect Leaders

Essence Of Mathematics
Toolness Of Mathematics
The Number Line
Variables
Equations
Functions

The Windflower Saga
Who Am I?
Primordial Equilibrium
Primordial Care
Force Of Being
Forgiveness

Blessed are they that have not seen, and yet have believed. John 20:29