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<!doctype html>
<html lang="en">
<head>
<meta charset="utf-8">
<meta name="viewport" content="width=device-width, initial-scale=1">
<title>Final Temperature of a Mixture Calculator</title>
<link rel="icon" href="favicon.ico" type="image/x-icon">
<link rel="stylesheet" href="assets/css/bootstrap.css">
<link rel="stylesheet" href="assets/css/style.css" type="text/css">
<link rel="stylesheet" href="assets/css/fontawesome.css">
<link rel="stylesheet" href="assets/fontawesome/css/brands.css">
<link rel="stylesheet" href="assets/fontawesome/css/solid.css">
</head>
<body class="bg-pcode">
<header>
<div class="header"></div>
</header>
<section class="container">
<div class="jumbotron jumbotron-fluid mt-1 mb-1 shadow p-3 jumbo-bg">
<div class="container">
<h1 class="display-4 text-center text-wrap">Final Temperature Calculator for Mixtures</h1>
<p class="lead">Calculate the final temperature of a mixture of two liquids given their masses, specific heat capacities, and initial temperatures.</p>
<p>Start by selecting the known variables below and entering their values.</p>
</div>
</div>
</section>
<section class="container border border-info bg_cont mb-1">
<div class="row">
<h3 class="d-flex justify-content-center">Equation</h3>
</div>
<div class="row">
<div class="col-md-12 col-lg-12 col-xl-12">
<p class="d-flex justify-content-center">\[\LARGE T_{f} = \frac{m_1 c_1 T_{i1} + m_2 c_2 T_{i2}}{m_1 c_1 + m_2 c_2}\]</p>
</div>
</div>
</section>
<form id="SubmissionForm" novalidate>
<!-- Equation Selection -->
<section class="container border border-primary bg_cont mb-1">
<h4>Select the known variables:</h4>
<p>Please select the known variables from the options below and enter their values to calculate the final temperature of a mixture of two liquids. You can select any two variables to calculate the third. This calculator assumes that the two liquids
are well-mixed and that there is no heat loss to the surroundings.
</p>
<p>The above equation is used to calculate the final temperature of the mixture with:</p>
<p class="d-flex justify-content-center">
</p>
<ul>
<li>\(T_f\) is the final temperature of the mixture</li>
<li>\(m_1\) and \(m_2\) are the masses of the two liquids</li>
<li>\(c_1\) and \(c_2\) are the specific heat capacities of the two liquids</li>
<li>\(T_{i1}\) and \(T_{i2}\) are the initial temperatures of the two liquids</li>
</ul>
<div class="row align-items-center">
<div class="col-3 text-center">
<p class="fs-5 mb-0"><i class="fas text-success fa-check-square me-2"></i>Select the variables you know:
</p>
</div>
<div class="col-9">
<div class="ideal-check border p-3">
<div class="row">
<div class="col-6">
<div class="form-check form-switch border-bottom">
<input class="form-check-input" type="checkbox" value="same_liquid" id="same_liquid" name="same_liquid">
<label class="form-check-label" for="same_liquid">
Both liquids are the same
</label>
<a tabindex="0" class="btn btn-link" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Mixture 1 and Mixture 2:" data-bs-content="If both mixtures are the same liquids, you do not need to enter in the specific heat capacity. Click this checkbox and the specific heat capacity inputs won't be required.">
<i class="far fa-question-circle fa"></i>
</a>
</div>
</div>
</div>
</div>
</div>
</div>
</section>
<section class="container border border-primary bg_cont">
<div class="row d-flex justify-content-center">
<div class="card shadow-sm p-3 mt-1 mb-1" style="width: 26rem;">
<i class="fa-solid fa-vial fa-10x rounded mx-auto d-block mt-1 shadow-sm p-3"></i>
<div class="card-body">
<h4 class="text-center">Mixture 1<br>
<a tabindex="0" class="btn btn-link" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Mixture 1 (m<sub>1</sub>, c<sub>1</sub>, T<sub>i1</sub>):" data-bs-content="Enter the mass, specific heat capacity and the initial temperature of the 1st liquid in the mixture.">
<i class="far fa-question-circle fa"></i>
</a>
</h4>
<!-- Input 1 Mass 1 -->
<div class="form-group">
<div class="row">
<div class="col">
<label for="inputMass1" class="form-label">Mass (m<sub>1</sub>)</label>
<input type="number" name="inputMass1" id="inputMass1" class="reset_form formCheck maxAllow form-control input-rounded-start" aria-label="Enter the mass of the first liquid in the mixture. Check your units." data-input="mass1" required>
</div>
<div class="col">
<label for="unitsMass1" class="form-label">Units</label>
<select class="form-select" name="unitsMass1" id="unitsMass1" style="width:75px;" data-input="mass">
<option value="kg" selected>kg</option>
<option value="gm">g</option>
<option value="mg">mg</option>
<option value="μg">μg</option>
<option value="lb">lb</option>
<option value="oz">oz</option>
<option value="toz">t oz</option>
</select>
</div>
</div>
</div>
<!-- Input 2 - Specific Heat Capacity 1 -->
<div class="form-group">
<div class="row">
<div class="col">
<label for="inputSpecificHeatCapacity1" class="form-label">Specific Heat
(c<sub>1</sub>)</label>
<input type="number" name="inputSpecificHeatCapacity1" id="inputSpecificHeatCapacity1" class="reset_form formCheck maxAllow form-control input-rounded-start" aria-label="Enter the specific heat capacity of the first liquid in the mixture. Check your units. If you know the liquid being used, check the preset values available here."
data-input="temperature1">
</div>
<div class="col">
<label for="unitsSpecificHeatCapacity1" class="form-label">Units</label>
<select class="form-select" name="unitsSpecificHeatCapacity1" id="unitsSpecificHeatCapacity1" data-input="specificHeatCapacity1">
<option value="c1" selected>J kg⁻¹·K⁻¹</option>
<option value="c2">J g⁻¹·k⁻¹</option>
<option value="c4">cal g⁻¹·K⁻¹</option>
<option value="c5">Btu lb⁻¹·°F⁻¹</option>
<option value="c6">kJ kg⁻¹·K⁻¹</option>
<option value="c8">Water: 4186 J kg⁻¹·K⁻¹</option>
<option value="c9">Ethanol: 2440 J kg⁻¹·K⁻¹</option>
<option value="c13">Benzene: 1750 J kg⁻¹·K⁻¹</option>
<option value="c14">Chloroform: 1170 J kg⁻¹·K⁻¹</option>
<option value="c15">Diethyl ether: 1720 J kg⁻¹·K⁻¹</option>
<option value="c16">Glycerol: 2400 J kg⁻¹·K⁻¹</option>
<option value="c17">Hexane: 2220 J kg⁻¹·K⁻¹</option>
<option value="c18">Methanol: 2500 J kg⁻¹·K⁻¹</option>
<option value="c19">Nitric acid: 1460 J kg⁻¹·K⁻¹</option>
<option value="c20">Nitrogen dioxide: 1420 J kg⁻¹·K⁻¹</option>
<option value="c21">Phenol: 1280 J kg⁻¹·K⁻¹</option>
<option value="c22">Sulfuric acid: 1530 J kg⁻¹·K⁻¹</option>
<option value="c23">Toluene: 1240 J kg⁻¹·K⁻¹</option>
<option value="c24">Xylene: 1130 J kg⁻¹·K⁻¹</option>
</select>
</div>
</div>
</div>
<!-- Input 3 Temperature i1 -->
<div class="form-group">
<div class="row">
<div class="col">
<label for="inputTemperature1" class="form-label">Temperature
(T<sub>i1</sub>)</label>
<input type="number" name="inputTemperature1" id="inputTemperature1" class="reset_form formCheck maxAllow form-control input-rounded-start" aria-label="Enter the temperature of the first liquid in the mixture. Check your units." data-input="temperature1"
required>
</div>
<div class="col">
<label for="unitsTemperature1" class="form-label">Units</label>
<select class="form-select" name="unitsTemperature1" id="unitsTemperature1" style="width:75px;" data-input="temperature">
<option value="K" selected>K</option>
<option value="C">°C</option>
<option value="F">°F</option>
</select>
</div>
</div>
</div>
<!-- End Input 3 -->
</div>
</div>
<!-- Second Card -->
<div class="card shadow-sm p-3 mt-1 mb-1" style="width: 26rem;">
<i class="fa-solid fa-vials fa-10x rounded mx-auto d-block mt-1 shadow-sm p-3"></i>
<div class="card-body">
<h4 class="text-center">Mixture 2<br>
<a tabindex="0" class="btn btn-link" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Mixture 2 (m<sub>2</sub>, c<sub>2</sub>, T<sub>i2</sub>):" data-bs-content="Enter the mass, specific heat capacity and the initial temperature of the 2nd liquid in the mixture.">
<i class="far fa-question-circle fa"></i>
</a>
</h4>
<!-- Input 1 Mass 2 -->
<div class="form-group">
<div class="row">
<div class="col">
<label for="inputMass2" class="form-label">Mass (m<sub>2</sub>)</label>
<input type="number" name="inputMass2" id="inputMass2" class="reset_form formCheck maxAllow form-control input-rounded-start" aria-label="Enter the mass of the first liquid in the mixture. Check your units." data-input="mass2" required>
</div>
<div class="col">
<label for="unitsMass2" class="form-label">Units</label>
<select class="form-select" name="unitsMass2" id="unitsMass2" style="width:75px;" data-input="mass">
<option value="kg2" selected>kg</option>
<option value="gm2">g</option>
<option value="mg2">mg</option>
<option value="μg2">μg</option>
<option value="lb2">lb</option>
<option value="oz2">oz</option>
<option value="toz2">t oz</option>
</select>
</div>
</div>
</div>
<!-- Input 2 - Specific Heat Capacity 2 -->
<div class="form-group">
<div class="row">
<div class="col">
<label for="inputSpecificHeatCapacity2" class="form-label">Specific Heat
(c<sub>2</sub>)</label>
<input type="number" name="inputSpecificHeatCapacity2" id="inputSpecificHeatCapacity2" class="reset_form formCheck maxAllow form-control input-rounded-start" aria-label="Enter the specific heat capacity of the first liquid in the
mixture. Check your units. If you know the liquid being used, check the preset
values available here." data-input="temperature1">
</div>
<div class="col">
<label for="unitsSpecificHeatCapacity2" class="form-label">Units</label>
<select class="form-select" name="unitsSpecificHeatCapacity2" id="unitsSpecificHeatCapacity2" data-input="specificHeatCapacity2">
<option value="c12" selected>J kg⁻¹·K⁻¹</option>
<option value="c22">J g⁻¹·k⁻¹</option>
<option value="c42">cal g⁻¹·K⁻¹</option>
<option value="c52">Btu lb⁻¹·°F⁻¹</option>
<option value="c62">kJ kg⁻¹·K⁻¹</option>
<option value="c82">Water: 4186 J kg⁻¹·K⁻¹</option>
<option value="c92">Ethanol: 2440 J kg⁻¹·K⁻¹</option>
<option value="c132">Benzene: 1750 J kg⁻¹·K⁻¹</option>
<option value="c142">Chloroform: 1170 J kg⁻¹·K⁻¹</option>
<option value="c152">Diethyl ether: 1720 J kg⁻¹·K⁻¹</option>
<option value="c162">Glycerol: 2400 J kg⁻¹·K⁻¹</option>
<option value="c172">Hexane: 2220 J kg⁻¹·K⁻¹</option>
<option value="c182">Methanol: 2500 J kg⁻¹·K⁻¹</option>
<option value="c192">Nitric acid: 1460 J kg⁻¹·K⁻¹</option>
<option value="c202">Nitrogen dioxide: 1420 J kg⁻¹·K⁻¹</option>
<option value="c212">Phenol: 1280 J kg⁻¹·K⁻¹</option>
<option value="c222">Sulfuric acid: 1530 J kg⁻¹·K⁻¹</option>
<option value="c232">Toluene: 1240 J kg⁻¹·K⁻¹</option>
<option value="c242">Xylene: 1130 J kg⁻¹·K⁻¹</option>
</select>
</div>
</div>
</div>
<!-- Input 3 Temperature 2 -->
<div class="form-group">
<div class="row">
<div class="col">
<label for="inputTemperature2" class="form-label">Temperature
(T<sub>i2</sub>)</label>
<input type="number" name="inputTemperature2" id="inputTemperature2" class="reset_form formCheck maxAllow form-control input-rounded-start" aria-label="Enter the temperature of the first liquid in the mixture. Check your units." data-input="temperature2"
required>
</div>
<div class="col">
<label for="unitsTemperature2" class="form-label">Units</label>
<select class="form-select" name="unitsTemperature2" id="unitsTemperature2" style="width:75px;" data-input="temperature">
<option value="K2" selected>K</option>
<option value="C2">°C</option>
<option value="F2">°F</option>
</select>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
<div class="col text-center">
<button type="reset" class="btn-sm btn-outline-danger btn mb-2" id="resetButton1">Reset</button>
<a tabindex="0" class="btn btn-link" role="button" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Reset Form" data-bs-content="Reset the form to add new variables to calculate.">
<i class="far fa-question-circle fa mb-2"></i>
</a>
<button type="button" class="btn-sm btn btn-outline-success mb-2" id="submitButton" disabled>Calculate</button>
<a tabindex="0" class="btn btn-link" role="button" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Calculate" data-bs-content="Once you have added three variables submit the calculation for evaluation.">
<i class="far fa-question-circle fa mb-2"></i>
</a>
<div id="error"></div>
</div>
<br>
</section>
<!-- TABLE ONE - RESULTS -->
<section id="results_table_1" class="container border border-success mt-1 mb-1 bg_cont">
<h5>Table 1: Results in SI units</h5>
<table class="table table-sm">
<thead>
<tr>
<th scope="col" class="w50">Variable</th>
<th scope="col" class="w50">Amount</th>
</tr>
</thead>
<tr>
<td>Final Temperature (T<sub>f</sub>)</td>
<td id="temperatureOutput">K</td>
</tr>
<tr>
<td>Mass (m<sub>1</sub> + m<sub>2</sub>)</td>
<td id="massOutput">kg</td>
</tr>
<tr>
<td>Change in Temperature from T<sub>i1</sub> (ΔT<sub>i1</sub>)</td>
<td id="changeInTemperatureOutput1">K</td>
</tr>
<tr>
<td>Change in Temperature from T<sub>i2</sub> (ΔT<sub>i2</sub>)</td>
<td id="changeInTemperatureOutput2">K</td>
</tr>
</tbody>
</table>
<h6 class="equation_color">Equation Used:</h6>
<p id="equation"></p>
<p id="substitutedNumbers"></p>
<button type="reset" class="btn-sm btn-outline-danger btn mb-2" id="resetButton2">Reset</button>
<a tabindex="0" class="btn btn-link" role="button" data-bs-toggle="popover" data-bs-trigger="focus" data-bs-title="Reset Form" data-bs-content="Reset the form to add new variables to calculate. The answer will remain here until you calculate a new set of variables.">
<i class="far fa-question-circle fa mb-2"></i>
</a>
<br>
<p><em>Table 1 provides the SI unit for each variable. You can change the output accordingly and see the
common unit conversions in Table 2.</em></p>
</section>
</form>
<!-- Table 2 Results Table -->
<section class="container border border-success mt-1 mb-2 bg_cont">
<h5>Table 2: Results with common units displayed</h5>
<table class="table table-sm">
<thead>
<tr class="t_line">
<th scope="col" class="w50">Variable</th>
<th scope="col" class="w50">Amount</th>
</tr>
</thead>
<tbody>
<tr>
<td>Mass (m<sub>1</sub>)</td>
<td id="m1x">kg</td>
</tr>
<tr>
<td></td>
<td id="m2x">g</td>
</tr>
<tr>
<td></td>
<td id="m3x">mg</td>
</tr>
<tr>
<td></td>
<td id="m4x">μg</td>
</tr>
<tr>
<td></td>
<td id="m5x">lb</td>
</tr>
<tr>
<td></td>
<td id="m6x">oz</td>
</tr>
<tr class="t_line">
<td></td>
<td id="m7x">t oz</td>
</tr>
<tr>
<td>Mass (m<sub>2</sub>)</td>
<td id="m1x2">kg</td>
</tr>
<tr>
<td></td>
<td id="m2x2">g</td>
</tr>
<tr>
<td></td>
<td id="m3x2">mg</td>
</tr>
<tr>
<td></td>
<td id="m4x2">μg</td>
</tr>
<tr>
<td></td>
<td id="m5x2">lb</td>
</tr>
<tr>
<td></td>
<td id="m6x2">oz</td>
</tr>
<tr class="t_line">
<td></td>
<td id="m7x2">t oz</td>
</tr>
<tr>
<td>Heat Capacity (c<sub>1</sub>)</td>
<td id="c1x">J kg⁻¹·K⁻¹</td>
</tr>
<tr>
<td></td>
<td id="c3x">J g⁻¹·k⁻¹</td>
</tr>
<tr>
<td></td>
<td id="c4x">cal g⁻¹·K⁻¹</td>
</tr>
<tr>
<td></td>
<td id="c5x">Btu lb⁻¹·°F⁻¹</td>
</tr>
<tr class="t_line">
<td></td>
<td id="c6x">kJ kg⁻¹·K⁻¹</td>
</tr>
<tr>
<td>Heat Capacity (c<sub>2</sub>)</td>
<td id="c1x2">J kg⁻¹·K⁻¹</td>
</tr>
<tr>
<td></td>
<td id="c3x2">J g⁻¹·k⁻¹</td>
</tr>
<tr>
<td></td>
<td id="c4x2">cal g⁻¹·K⁻¹</td>
</tr>
<tr>
<td></td>
<td id="c5x2">Btu lb⁻¹·°F⁻¹</td>
</tr>
<tr class="t_line">
<td></td>
<td id="c6x2">kJ kg⁻¹·K⁻¹</td>
</tr>
<tr>
<td>Initial Temperature 1 (T<sub>i1</sub>)</td>
<td id="t1x">K</td>
</tr>
<tr>
<td></td>
<td id="t2x">°C</td>
</tr>
<tr class="t_line">
<td></td>
<td id="t3x">°F</td>
</tr>
<tr>
<td>Initial Temperature 2 (T<sub>i2</sub>)</td>
<td id="t1x2">K</td>
</tr>
<tr>
<td></td>
<td id="t2x2">°C</td>
</tr>
<tr class="t_line">
<td></td>
<td id="t3x2">°F</td>
</tr>
<tr>
<td>Final Temperature (T<sub>f</sub>)</td>
<td id="tf1x">K</td>
</tr>
<tr>
<td></td>
<td id="tf2x">°C</td>
</tr>
<tr>
<td></td>
<td id="tf3x">°F</td>
</tr>
</tbody>
</table>
<p><em>Table 2 shows the results of all the calculations and various units available with all conversions
completed.</em>
</p>
</section>
</div>
<div id="alert-container">
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