A 16.0 gallon steel tank is topped off with gasoline at 0 degrees C. With the lid off, the tank is left outside where the air temp is a sizzling 40.0 deg C. How much gasoline overflows? (assume a=12.0x10^-6/degree C for steel, B=950.0x10^-6/deg C for gasoline). Don't forget the expansion of the steel tank.

To find out how much gasoline overflows, we need to calculate the change in volume of both the steel tank and the gasoline.

First, let's calculate the change in volume of the steel tank. We can use the formula:

ΔV = V0 * α * ΔT

Where:
ΔV is the change in volume of the steel tank
V0 is the initial volume of the steel tank
α is the coefficient of linear expansion for steel
ΔT is the change in temperature

Given:
V0 = 16.0 gallons (initial volume)
α = 12.0x10^-6/°C (coefficient of linear expansion for steel)
ΔT = 40.0 - 0 = 40.0°C (change in temperature)

Using the formula, we can calculate the change in volume of the steel tank:

ΔV = 16.0 gallons * 12.0x10^-6/°C * 40.0°C
ΔV = 7.68x10^-3 gallons

Next, let's calculate the change in volume of the gasoline. We can use a similar formula:

ΔV = V0 * β * ΔT

Where:
ΔV is the change in volume of the gasoline
V0 is the initial volume of the gasoline (which is the same as the initial volume of the steel tank, 16.0 gallons)
β is the coefficient of volume expansion for gasoline
ΔT is the change in temperature (same as before, 40.0°C)

Given:
V0 = 16.0 gallons
β = 950.0x10^-6/°C

Using the formula, we can calculate the change in volume of the gasoline:

ΔV = 16.0 gallons * 950.0x10^-6/°C * 40.0°C
ΔV = 0.608 gallons

Finally, to find out how much gasoline overflows, we need to subtract the change in volume of the steel tank from the change in volume of the gasoline:

Overflow = ΔV_gasoline - ΔV_steel
Overflow = 0.608 gallons - 7.68x10^-3 gallons
Overflow ≈ 0.600 gallons

Therefore, approximately 0.600 gallons of gasoline overflows from the tank.