Thermal expansion: The coefficient of linear expansion of aluminum is 24 × 10^-6 K^-1 and the coefficient of volume expansion of olive oil is 0.68 × 10^-3K^-1. A novice cook, in preparation for deep-frying some potatoes, fills a 1.00-L aluminum pot to the brim and heats the oil and the pot from an initial temperature of 15°C to 190°C. To his consternation some olive oil spills over the top. How much? A) 0.11 L B) 0.12 L C) 0.13 L D) 0.14 L E) 0.15 L

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The volume of the oil increases by:$$V_f - V_i = \beta V_i (T_f - T_i)$$$$= (0.68 	imes 10^{-3} 	ext{ K}^{-1})(1.00 	ext{ L})(190\degree 	ext{C} - 15\degree 	ext{C})$$$$= 0.119 	ext{ L}$$The volume of the aluminum pot increases by:$$V_f - V_i = \beta V_i (T_f - T_i)$$$$= (24 	imes 10^{-6} 	ext{ K}^{-1})(1.00 	ext{ L})(190\degree 	ext{C} - 15\degree 	ext{C})$$$$= 0.00432 	ext{ L}$$The total volume increase is:$$0.119 	ext{ L} + 0.00432 	ext{ L} = 0.123 	ext{ L}$$Therefore, the amount of olive oil that spills over the top is:$$0.123 	ext{ L} - 1.00 	ext{ L} = 0.123 	ext{ L}$$

Thermal Expansion: the Coefficient of Linear Expansion of Aluminum Is