Gas tank in the sun
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The following quantities appear in the problem:
Temperatur \(T\) / Volumen \(V\) / Längenausdehnungskoeffizient \(\alpha\) / Volumenausdehnungskoeffizient \(\gamma\) /
The following formulas must be used to solve the exercise:
\(V = V_0 \cdot (1+ 3\alpha \cdot \Delta\vartheta) \quad \) \(V = V_0 \cdot (1+ \gamma \cdot \Delta\vartheta) \quad \)
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Exercise:
The VzO steel aStO gas tank of a car is filled to the top with gasoline aGaO at TaO. The car sits in the sun and the tank reaches a temperature of TbO. How much gasoline do you expect to overflow from the tank? One US gallon is approximately .liter.
Solution:
At the new temperature the steel tank has SolQtydTTbX-TaXK SolQtyVTVX*+*aStX*dTXcubicmeter sscVT V_ +alpha Delta theta V + aSt dT VT Volume and the gasoline has SolQtyVGVX*+aGaX*dTXcubicmeter sscVG V_ +gammaDelta theta V +aGa dT VG We expect therefore SolQtydVVGX-VTXcubicmeter Delta V sscVG - sscVG VG - VT dV to overflow.
The VzO steel aStO gas tank of a car is filled to the top with gasoline aGaO at TaO. The car sits in the sun and the tank reaches a temperature of TbO. How much gasoline do you expect to overflow from the tank? One US gallon is approximately .liter.
Solution:
At the new temperature the steel tank has SolQtydTTbX-TaXK SolQtyVTVX*+*aStX*dTXcubicmeter sscVT V_ +alpha Delta theta V + aSt dT VT Volume and the gasoline has SolQtyVGVX*+aGaX*dTXcubicmeter sscVG V_ +gammaDelta theta V +aGa dT VG We expect therefore SolQtydVVGX-VTXcubicmeter Delta V sscVG - sscVG VG - VT dV to overflow.