Early in the morning, when the temperature is 5.0°C, gasoline is pumped into the 51-liter steel tank of a car until it is filled to the top. Later in the day the temperature rises to 25°C. Given that the coefficient of volume expansion is 0.95 * 10-3 °C-1 for gasoline and 0.036 * 10-3 °C-1 for steel, how much gasoline spills out of the tank?

gasoline spills out of the tank is 0.93228 L

Explanation:

Given data

temperature T1 = 5.0°C

temperature rises T2 = 25°C

volume = 51 L

coefficient of volume expansion gasoline = 0.95 * 10-3 °C-1

coefficient of volume expansion steel = 0.036 * 10-3 °C-1

to find out

how much gasoline spills out of the tank

solution

we know that

the volume of liquid spills out from tank is given by expression as

change in volume in gas - change in volume in tank

so

change in volume of gas

ΔV = V * ΔT * β

put value

ΔV = 51 * (20) * 950 * 10^-6

ΔV = 0.969 L

and

change in volume of steel tank

ΔV = V * ΔT * β

ΔV = 51 * (20) * 36 * 10^-6

ΔV = 0.03672 L

so gasoline spills out of the tank is = 0.969 - 0.03672

gasoline spills out of the tank is 0.93228 L