Containers for liquids have interior volumes that are largerthan their rated capacity. This is necessary to allow for expansionof the liquid contents as the temperature changes. You have a fivegallon steel fuel can manufactured to have an interior volume of5.22 gallons (19.76 L). The coefficient of thermal expansion ofsteel is small enough that this volume will not changesignificantly with temperature in this problem.
One cold spring morning, you pump 5.00 gallons (18.93 L) ofgasoline into your fuel can, leaving 0.22 gallons (0.83 L)unfilled. The gasoline comes from an underground tank at 54.9°F(12.7°C, 285.9 K), but the outside temperature is 31°F (-0.6°C,272.6 K). You then screw on the cap tightly and leave the canoutside. The weather forecast calls for the temperature to stayconstant in the morning morning, followed by a significant warmingtrend in the afternoon, when the temperature will rise to a high of75°F (23.9°C, 297.0 K). The atmospheric pressure will stay constantat 973 mbar (97.3 kPa) all day.
1. Gasoline has a coefficient of thermal expansion of 9.50 x10^-4/°C. What will the unfilled volume in your fuel can be afterthe gasoline cools in the morning?
2. What will the absolute pressure of the air in the sealed fuelcan be then?
3. What will the unfilled volume in your fuel can be when thegasoline and air in the fuel can warm to the afternoon hightemperature?
4. What will the absolute pressure of the air in the sealed fuelcan be then, assuming no air can escape?
5. Your fuel can actually has a safety gasket which will allowair to leave the can if the pressure difference to the outside(called the “gauge pressureâ€) exceeds 5.0 psi (34 kPa). Will thesafety gasket vent air from the fuel can in the afternoon?
