Suppose your 48.0 L (12.7 gal) steel gasoline tank is full of gas, both the tank

Question

Suppose your 48.0 L (12.7 gal) steel gasoline tank is full of gas, both the tank and the gas have a temperature of 15.0°C. The coefficient of volume expansion for gasoline is 950 106/°C and for steel is 35 106/°C. (a) How much gas has spilled by the time they warm to 48.0°C? Correct: Your answer is correct. L (b) Suppose the 48.0 L tank is sealed, preventing the gasoline from overflowing. What pressure would be created in the gasoline tank if the sealed tank increases in temperature from 15.0°C to 48.0°C? (Use 1.00 x109 N/m2 as the bulk modulus for gasoline.) Need help with the second part.

Explanation / Answer

We know that

The change in the volume of the steel is given by =(35 106/°C)(48-15)=1155*10-6

The change in the volume of gas = 950 106/°C(48-15) =31350*10-6

The excess volume change is given by =30195*10-6*Original volume =30195*10-6*48L =1.44L

The change in volume =1.44L

Therefore the bulk modulus is given by

K =dp/(dV/V)

dp =k*(dv/v) =1.00 x109 N/m2*(1.44/48) =30195000=3.019*109Pa

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