Calculating Thermal Expansion: Gas vs. Gas Tank

The tank and gasoline increase in volume, but the gasoline increases more, so the amount spilled is the difference in their volume changes. (The gasoline tank can be treated as solid steel.) We can use the equation for volume expansion to calculate the change in volume of the gasoline and of the tank.

1. Use the equation for volume expansion to calculate the increase in volume of the steel tank:

2. The increase in volume of the gasoline is given by this equation:

3. Find the difference in volume to determine the amount spilled as

Alternatively, we can combine these three equations into a single equation. (Note that the original volumes are equal.)

This amount is significant, particularly for a 60.0-L tank. The effect is so striking because the gasoline and steel expand quickly. The rate of change in thermal properties is discussed in Heat and Heat Transfer Methods.

If you try to cap the tank tightly to prevent overflow, you will find that it leaks anyway, either around the cap or by bursting the tank. Tightly constricting the expanding gas is equivalent to compressing it, and both liquids and solids resist being compressed with extremely large forces. To avoid rupturing rigid containers, these containers have air gaps, which allow them to expand and contract without stressing them.