I mean, should I refuel my vehicle in the morning?
The reasoning is simple, in the morning the temperature is low and the density of the fuel would be higher and I get more energy per litre(or whatever metric system you use). But in afternoon, or by evening, the temperature increases and the density decreases, thus reducing the energy per litre.
(I have tried Google, but couldn't find any satisfactory answers, or could only find conflicting answers.)
According to wikpedia, the volumetric constant of thermal expansion for gasoline is
av=950*10^-6/K
For example, if the temperature changes by 20K (20°C; 36°F), the volume changes by a factor of
950*10^-6/K * 20K = 0.0192
The warmer fuel has a volume increased by about 2%, and since energy content depends on the mass, the energy per volume decreases by about 2%.
But this doesn't mean you get more for your money in the morning. Most fuel stations have their tanks under ground, where the temperature is quite constant over the day.
Temperature in the tanks of the gas station can change significantly when they are refilled from a tank truck, but since you usually don't know when the truck comes, nor how much new fuel is dumped into which tank, you can't save money here.
At least in Europe, more and more gas pumps are temperature compensated, i.e. they don't display the actual volume, but the volume the fuel would have at 15°C (59°F). In this case, there is no way to get more for the money.
Many countries (but notably not US) actually have regulations regarding temperature compensation of fuel volume. For example, UK has Standard temperature accounting for fuel dispensers, which allows the volumetric measurements to be corrected for the standard temperature of 15°C. Needless to say, it makes no difference when to tank in this case, as you essentially pay for the mass of the fuel, even if it is measured in litres.
Even in the US, it won't make any practical difference between mornings and afternoons (but it will make some difference for summer vs winter). From Wikipedia:
Modern tanks are non-metallic and sealed to stop leaks. Some have double walls or other structures that provide inadvertent thermal insulation while pursuing the main goal of keeping gasoline out of the soil around the tank. The net result is that while the air temperature can easily vary between 30 and 85 °F (−1 and 29 °C), the gasoline in the insulated tank changes temperature much more slowly
As @sweber said, the tanks are usually underground, which keeps their temperature constant. However, if you are filling a smaller bottle with gasoline (ex: for a small engine), the first few gallons (litres) that come out of the nozzle will be a slightly different temperature.
This is because the pumps are above ground, and if they are sitting in the sun, they will be even more effected by morning-evening temperatures.
However, if you are filling totally up, professionals have determined that it makes next to no difference to the average consumer.
It doesn't make ANY difference to the cost
If you read the small print on the pump, you'll find the cost per volume advertised is actually based on a particular temperature and density. If the density is different for any reason this is automatically accounted for in the price you pay.
So the actual price you pay for a particular amount of fuel will be the same regardless of the volume that fuel actually occupies.
