Problem 1. Pressure is defined as force per unit area. Newton\'s Second Law tell

Question

Problem 1. Pressure is defined as force per unit area. Newton's Second Law tells us that forc is mass multiplied by acceleration, while acceleration is the first time derivative of yelocity (o the second time derivative of distance). Therefore the units of acceleration are m/s A unit o force has the dimensions of kg.m/s2, and a unit of pressure has the dimensions of kg.m/s2.m2 o kg/m.sz. The basic unit of pressure is Pascal (Pa, 1Pa 1 kg/m s Atmospheric pressure i Now the problem: the gas constant for dry air d is 287 2, 2 (here K stands fo R degrees Kelvin, KE Celsius 273). Assuming the temperature is 320 K and the pressure i 1000 hPa, what is the atmospheric density? CHint: Do not try to look up the formula. Writ down all variables you are given, together with their units. Figure out how to combine them t get the density. Show all your unit conversions.) (10 pts.)

Explanation / Answer

as Force F = ma = Kgm/s^2

Pressure P = F/A = Kgm/(s^2 *m^2)

so presusure P has dimensions of ------> Kg/ms^2

atmospheric density = density of air = mass/voume = kg/m^3

writing density rho as desnity = P/RT

Dimensionally rho = Kg/ms^2 /(m^2 /s^2 .K)

rho = kg/m^3

so

Now by substitution

density rho = 1000*100/(287 * 320)

rho = 1.088 kg/m^3 ----------------<<<<<<<<<<<<<<<<Answer

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