You are making pesto for your pasta and have a cylindrical measuring cup 10.7 cm

Question

You are making pesto for your pasta and have a cylindrical measuring cup 10.7 cm high made of ordinary glass (=2.7×105(C)1) that is filled with olive oil (=6.8×104(C)1) to a height of 1.10 mm below the top of the cup. Initially, the cup and oil are at a kitchen temperature of 21.4 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?

Express your answer in degrees Celsius to three significant figures.

Explanation / Answer

Olive oil will start to spill out of the cup when volume of oil greater than volume of cup.

Volume of oil = Volume of cup

Voil = Vcup

Aoilhoil[ 1+oil(Tf – Ti)] = Acuphcup[ 1+cup(Tf – Ti)]

Since Aoil =Acup

hoil[ 1+oil(Tf – Ti)] = hcup[ 1+cup(Tf – Ti)]

(10.7*10^-2 – 1.10*10^-3)[1+6.8*10^-4(Tf – 21.4)] = (10.7*10^-2)[1+2.7*10^-5(Tf – 21.4)]

Tf = 37.3 oC

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