I pull into a gas station and fill up my tank to the very top.The temperature of the gasoline is 10 $\circ$ C at that time.Exactly 56 liters fit into my tank.I live next door to the gas station,and I use practically no gas for the short drive into my garage.My garage is at 20 $\circ$ C,and the gas warms up to that temperature.How much gas will overflow from my tank onto the garage floor? (Assume that the gas tank of my car was at 20 $\circ$ C all along and does not change its shape during this process.The coefficient of volume expansion of gasoline is 0.95·10^-3 /K.) A)0 liter B)0.53 liter C)1.79 liter D)0.95 liter E)2.33 liter

Question

Quizplus · Accepted Answer

The volume expansion of the gasoline can be calculated using the formula: $\Delta V = \beta V_0 \Delta T$, where $\beta$ is the coefficient of volume expansion, $V_0$ is the initial volume, and $\Delta T$ is the change in temperature. Given $\beta = 0.95 \times 10^{-3} /K$, $V_0 = 56$ liters, and $\Delta T = 20°C - 10°C = 10°C$, the overflow volume $\Delta V = 0.95 \times 10^{-3} \times 56 \times 10 = 0.532$ liters, which rounds to 0.53 liters.

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