Problem 56333. Air Density from Temperature and Pressure

Created by Meg Noah

Solve Later

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0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">The density of air can be estimated from the product of molar mass and molar density:</span></span></div><div style="block-size: 22.5px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 11.25px; text-align: left; transform-origin: 384px 11.25px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="vertical-align:-6px"><img 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src="data:image/png;base64,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" width="130" height="20" style="width: 130px; height: 20px;"></span></div><div style="block-size: 84px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 42px; text-align: left; transform-origin: 384px 42px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Write a function that finds the density of air in kg per cubic meter, for input temperature (in Kelvin) and pressure (in mb).  This function should allow: a single input temperature and pressure pair, a single temperature and vector of pressures, a single pressure and and a vector of temperatures, a vector of pressures and a vector of temperatures of the same size (interpreted as pairs).  Return -1 if a P and T are unequal vector dimensions greater than 1.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Note: convert values to </span></span><span style="vertical-align:-5px"><img src="data:image/png;base64,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" width="40" height="19" style="width: 40px; height: 19px;"></span><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">.</span></span></div><div style="block-size: 21px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 10.5px; text-align: left; transform-origin: 384px 10.5px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">Note:</span></span></div><div style="block-size: 42px; font-family: Helvetica, Arial, sans-serif; line-height: 21px; margin-block-end: 9px; margin-block-start: 2px; margin-bottom: 9px; margin-inline-end: 10px; margin-inline-start: 4px; margin-left: 4px; margin-right: 10px; margin-top: 2px; perspective-origin: 384px 21px; text-align: left; transform-origin: 384px 21px; white-space: pre-wrap; margin-left: 4px; margin-top: 2px; margin-bottom: 9px; margin-right: 10px; "><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style="">See </span></span><a target='_blank' href = "https://www.mathworks.com/matlabcentral/cody/problems/56328-molar-air-density-from-temperature-and-pressure"><span style=""><span style="">Problem 56328. Molar Air Density from Temperature and Pressure</span></span></a><span style="block-size: auto; display: inline; margin-block-end: 0px; margin-block-start: 0px; margin-bottom: 0px; margin-inline-end: 0px; margin-inline-start: 0px; margin-left: 0px; margin-right: 0px; margin-top: 0px; perspective-origin: 0px 0px; transform-origin: 0px 0px; "><span style=""> for explanation of how to find the molar density of air can be found from the Temperature and Pressure using the ideal gas law.</span></span></div></div></div>

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Rafael S.T. Vieira on 29 Oct 2022

Each problem should be self-contained. Requiring the users to go to different places even within the same site may create inconsistencies years later when not even you remember about it anymore.

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Problem 56333. Air Density from Temperature and Pressure

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