Car mechanics use compressed air tools to open bolts. Instead of using an air compressor one can also use a tank of pressurized air. There is an air tank with a volume of 50 L to work with. The pressure of the tank is 50 bars when it is stored indoors at 20 °C. The bolt wrench needs at least 10 bar pressure to operate.
How long can the mechanics use the bolt wrench outdoors at -20 °C if it consumes 200 L/min of air at normal pressure ? the normal pressure is 1.0 bar.
The Attempt at a Solution
R = 8.314E-2 L bar/(mol K)
the tank holds this many moles
n = PV/RT = 50(50) / (8.314E-2 * 293) = 102.6 mol of air
at -20° the pressure will be
P = nRT/V = 102.6(8.31E-2)(253)/50 = 43.174 bar
How many moles can be delivered from 43.174 bar down to 10 bar, the lower limit?
all else being equal, moles are proportional to pressure
X mol / 102.6 mol = 10 bar / 43.174 bar
X mol = 23.76 mol (useful amount of gas)
How much does the wrench use per minute?
n = PV/RT = 1.0 (200) / (8.314E-2 * 253) = 9.508 mol per minute
23.76 mol / 9.508 mol/min = 2.499 or 2.5 min to 2 sig figs or 150 s
Is the solution correct ?