Problem 45411. Compute the missing quantity among P, V, T for an ideal gas

Created by Karl Ezra Pilario

Solve Later

{"relationships":[{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/document","targetMode":"","relationshipId":"rId1","target":"/matlab/document.xml"},{"relationshipType":"http://schemas.mathworks.com/matlab/code/2013/relationships/output","targetMode":"","relationshipId":"rId2","target":"/matlab/output.xml"}],"parts":[{"partUri":"/matlab/document.xml","relationship":[],"contentType":"application/vnd.mathworks.matlab.code.document+xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\"?>\n<w:document xmlns:w=\"http://schemas.openxmlformats.org/wordprocessingml/2006/main\"><w:body><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Consider 100 mol of helium gas at a certain pressure (P), volume (V), and temperature (T). Assuming that the ideal gas law applies, can you compute one of the 3 quantities given the other two?</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Recall that, with SI units, the ideal gas law is given by:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[P x V = n x R x T\n where:\n P = pressure [Pa] or [kg/m/s^2]\n V = volume [m^3]\n n = number of moles [mol]\n R = gas constant, 8.314 [J/mol/K] or [kg.m^2/K/mol/s^2]\n T = temperature [K]]]></w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Write a function that takes a MATLAB variable, x, which is always a 3-element row vector containing the values of P, V, T in that order. However, exactly one of these values will be NaN, which you must solve using the ideal gas law equation above, given the other two values. All inputs are given in SI units, hence, you can use the given value of</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>R</w:t></w:r><w:r><w:t> above. Note that</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>n</w:t></w:r><w:r><w:t> = 100 mol. You are ensured that P, V, and/or T are floating-point numbers with 2 decimal places that satisfy the following constraints:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>1 x 10^5 &lt;= P &lt;= 3 x 10^5</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>1 &lt;= V &lt;= 10</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"ListParagraph\"/><w:numPr><w:numId w:val=\"1\"/></w:numPr></w:pPr><w:r><w:t>300 &lt;= T &lt;= 500</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"text\"/></w:pPr><w:r><w:t>Output the value of the missing quantity rounded to 2 decimal places, followed by a space, and then the correct units, either</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>Pa</w:t></w:r><w:r><w:t>,</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>m^3</w:t></w:r><w:r><w:t>, or</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>K</w:t></w:r><w:r><w:t>. For this, you can use</w:t></w:r><w:r><w:t> </w:t></w:r><w:r><w:rPr><w:rFonts w:cs=\"monospace\"/></w:rPr><w:t>sprintf</w:t></w:r><w:r><w:t>. See sample test cases:</w:t></w:r></w:p><w:p><w:pPr><w:pStyle w:val=\"code\"/></w:pPr><w:r><w:t><![CDATA[>> idealgas([233424.06 NaN 435.02])\nans =\n '1.55 m^3'\n>> idealgas([109238.31 2.76 NaN])\nans =\n '362.64 K'\n>> idealgas([NaN 1.19 411.97])\nans =\n '287825.09 Pa']]></w:t></w:r></w:p></w:body></w:document>"},{"partUri":"/matlab/output.xml","contentType":"text/xml","content":"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\" ?><embeddedOutputs><metaData><evaluationState>manual</evaluationState><layoutState>code</layoutState><outputStatus>ready</outputStatus></metaData><outputArray type=\"array\"/><regionArray type=\"array\"/></embeddedOutputs>"}]}

Consider 100 mol of helium gas at a certain pressure (P), volume (V), and temperature (T). Assuming that the ideal gas law applies, can you compute one of the 3 quantities given the other two?Recall that, with SI units, the ideal gas law is given by:<pre class="language-matlab">P x V = n x R x T
 where:
 P = pressure [Pa] or [kg/m/s^2]
 V = volume [m^3]
 n = number of moles [mol]
 R = gas constant, 8.314 [J/mol/K] or [kg.m^2/K/mol/s^2]
 T = temperature [K]
</pre>Write a function that takes a MATLAB variable, x, which is always a 3-element row vector containing the values of P, V, T in that order. However, exactly one of these values will be NaN, which you must solve using the ideal gas law equation above, given the other two values. All inputs are given in SI units, hence, you can use the given value of <tt>R</tt> above. Note that <tt>n</tt> = 100 mol. You are ensured that P, V, and/or T are floating-point numbers with 2 decimal places that satisfy the following constraints:<ul><li>1 x 10^5 &lt;= P &lt;= 3 x 10^5</li><li>1 &lt;= V &lt;= 10</li><li>300 &lt;= T &lt;= 500</li></ul>Output the value of the missing quantity rounded to 2 decimal places, followed by a space, and then the correct units, either <tt>Pa</tt>, <tt>m^3</tt>, or <tt>K</tt>. For this, you can use <tt>sprintf</tt>. See sample test cases:<pre class="language-matlab">&gt;&gt; idealgas([233424.06 NaN 435.02])
ans =
 '1.55 m^3'
&gt;&gt; idealgas([109238.31 2.76 NaN])
ans =
 '362.64 K'
&gt;&gt; idealgas([NaN 1.19 411.97])
ans =
 '287825.09 Pa'
</pre>

Consider 100 mol of helium gas at a certain pressure (P), volume (V), and temperature (T). Assuming that the ideal gas law applies, can you compute one of the 3 quantities given the other two?

Recall that, with SI units, the ideal gas law is given by:

P x V = n x R x T
    where:
    P = pressure [Pa] or [kg/m/s^2]
    V = volume [m^3]
    n = number of moles [mol]
    R = gas constant, 8.314 [J/mol/K] or [kg.m^2/K/mol/s^2]
    T = temperature [K]

Write a function that takes a MATLAB variable, x, which is always a 3-element row vector containing the values of P, V, T in that order. However, exactly one of these values will be NaN, which you must solve using the ideal gas law equation above, given the other two values. All inputs are given in SI units, hence, you can use the given value of |R| above. Note that |n| = 100 mol. You are ensured that P, V, and/or T are floating-point numbers with 2 decimal places that satisfy the following constraints:

* 1 x 10^5 <= P <= 3 x 10^5
* 1 <= V <= 10
* 300 <= T <= 500

Output the value of the missing quantity rounded to 2 decimal places, followed by a space, and then the correct units, either |Pa|, |m^3|, or |K|. For this, you can use |sprintf|. See sample test cases:

>> idealgas([233424.06 NaN 435.02])
ans =
    '1.55 m^3'
>> idealgas([109238.31 2.76 NaN])
ans =
    '362.64 K'
>> idealgas([NaN 1.19 411.97])
ans =
    '287825.09 Pa'

Solve

Solution Stats

176 Solutions
46 Solvers

Last Solution submitted on Jun 12, 2021

Last 200 Solutions

Problem Comments

Problem Recent Solvers46

Problem Tags

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Problem 45411. Compute the missing quantity among P, V, T for an ideal gas

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers46

Suggested Problems

More from this Author19

Problem Tags

Community Treasure Hunt

Problem 45411. Compute the missing quantity among P, V, T for an ideal gas

Solution Stats

Last 200 Solutions

Problem Comments

Problem Recent Solvers46

Suggested Problems

More from this Author19

Problem Tags

Community Treasure Hunt

Players