You are making pesto for your pasta and have a cylindrical measuring cup 10.0 cm high made of ordinary glass [β=2.7×10−5(C∘)−1] that is filled with olive oil [β=6.8×10−4(C∘)−1] to a height of 3.00 mm below the top of the cup. Initially, the cup and oil are at room temperature (22.0∘C). You get a phone call and forget about the olive oil, which you inadvertently leave on the hot stove. The cup and oil heat up slowly and have a common temperature. At what temperature will the olive oil start to spill out of the cup?

The temperature will the olive oil start to spill out of the cup is 51.4 C

Explanation:

Knowing

βglass = .... βoil = .... T1 = 20

Knowing the coefficient volume expansion of oil is greater than glass

δVoil =  δVglass +

Using the first equation and

δVoil = δVoil * βoil * δT

δVglass = δVglass * βglass * δT

δT(δVoil * βoil - δVglass * βglass) =

Solving

δT =

T2 = T1 + δT

T2 = 20 + 31.4 = 51.4 C

this means that the temperature of both substances will be equal

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