Question

On a summer day in Narragansett, Rhode Island, the air temperature is 74 F and the barometric pressure is 14.5 lbf/in . Estimate the air density in kg/m.

Answer 1

There are some mistakes in the question as units pressure and air density are not written correctly.The correct question is here

On a summer day in Narragansett, Rhode Island, the air temperature is 74°F and the barometric pressure is 14.5 lbf/in². Estimate the air density in kg/m³.

Answer:

p=1.175 kg/m³

Explanation:

Given data

Temperature =74 F

Barometric pressure=14.5 lbf/in²

To find

Air density

Solution

From ideal gas law

$pV=mRT\\p=(m/V)RT$

As mass/volume is pressure So

$p=\frac{P}{RT}$

First we need to convert barometric pressure lbf/in² to N/m²

So

$Pressure=(14.5lbf/in^{2} )*(\frac{6894.76N/m^{2} }{lbf/in^{2} } )\\Pressure=99974.02N/m^{2}$

Now Substitute the given value and pressure to find air density

$p=\frac{P}{RT}\\ p=\frac{99974.02N/m^{2} }{(287J/kg.K)(\frac{74^{o}F-32}{1.8}+273.15 )}\\ p=\frac{99974.02N/m^{2} }{(287J/kg.K)*296.48K}\\ p=1.175kg/m^{3}$