Fluid Mechanics Air at standard sealevel pressure has a temp

Fluid Mechanics

Air at standard sea-level pressure has a temperature of 200 degrees C. What is the specific weight of the air?

The answer is 7.23 N/m^3, but I can\'t figure out how to work the problem.

Solution

The ideal gas law for dry air is P= dRT

Where R is the gas constant of dry air = 287 J K^-1kg^-1

d is density of dry air and T is temperature

The air pressure at sea level is 100000 pascals

Therefore density of air at sea level d= P/RT = 100000/(287x ( 200+273)) = 0.736643kg/m^3

Specific weight of air = d x g = 0.736643 x 9.8 = 7.22 N/m^3