Question

Containers for liquids have interior volumes that are larger than their rated capacity. This is necessary to allow for expansion of the liquid contents as the temperature changes. You have a five gallon steel fuel can manufactured to have an interior volume of 5.22 gallons (19.76 L). The coefficient of thermal expansion of steel is small enough that this volume will not change significantly with temperature in this problem.

One cold spring morning, you pump 5.00 gallons (18.93 L) of gasoline 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 can outside. The weather forecast calls for the temperature to stay constant in the morning morning, followed by a significant warming trend in the afternoon, when the temperature will rise to a high of 75°F (23.9°C, 297.0 K). The atmospheric pressure will stay constant at 973 mbar (97.3 kPa) all day.

1. Gasoline has a coefficient of thermal expansion of 9.50 x 10^-4/°C. What will the unfilled volume in your fuel can be after the gasoline cools in the morning?

2. What will the absolute pressure of the air in the sealed fuel can be then?

3. What will the unfilled volume in your fuel can be when the gasoline and air in the fuel can warm to the afternoon high temperature?

4. What will the absolute pressure of the air in the sealed fuel can be then, assuming no air can escape?

5. Your fuel can actually has a safety gasket which will allow air to leave the can if the pressure difference to the outside (called the “gauge pressure”) exceeds 5.0 psi (34 kPa). Will the safety gasket vent air from the fuel can in the afternoon?

Answer 1

Solution :

Given :

The Interior volume of the container=5.22 gallons(19.76L)

Volume of gasoline pumped=5 gallons(18.93L)

Remaining volume in container=0.22 gallons(0.83L)

Initial temperature of gasoline=54.9degrees F(285.9k,12.7degrees C)

Atmospheric pressure=973 mbar(97.3 kpa)

1)

So change in volume of gasoline in morning when temperature=

So unfilled volume = 5.22-4.936

=0.284 gallons

2)

PV=nRT

On a closed container 'n' remains constant.

So

3)

(volume at morning=4.936)

4)

5)

So the safety gasket will not vent air from the fuel can in the afternoon.