You just purchased a 400-l rigid tank for a client who works in the gas industry. the tank is delivered pre-filled with 3 kg of air at a temperature of 25c. assuming an atmospheric pressure of 98 kpa, determine the pressure reading if you connected a pressure gage to the tank.

the pressure reading when connected a pressure gauge is 543.44 kPa

Explanation:

Given data

tank volume (V) = 400 L i.e 0.4 m³

temperature (T) =  25°C  i.e. 25°C + 273 = 298 K

air mass (m)  = 3 kg

atmospheric pressure  = 98 kPa

To find out

pressure reading

Solution

we have find out pressure reading by gauge pressure

i.e. gauge pressure = absolute pressure - atmospheric pressure

first we find absolute pressure (p) by the ideal gas condition

i.e pV = mRT

p = mRT / V

p = ( 3 × 0.287 × 298 ) / 0.4

p = 641.44 kPa

so

gauge pressure = absolute pressure - atmospheric pressure

gauge pressure = 641.44 - 98

gauge pressure = 543.44 kPa