You are making pesto for your pasta and have a cylindrical measuring cup 10.0 cm high made of ordinary glass [$\beta = 2.7 \times 10{^-}{^5}(C^\circ){^-}{^1}]$ that is filled with olive oil [$\beta = 6.8 \times 10{^-}{^4}(C^\circ){^-}{^1}$] to a height of 3.00 mm below the top of the cup. Initially, the cup and oil are at room temperature 122.0$^\circ$C2. 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?

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at a common temperature. This problem asked what would be the temperature of that oil? Such that it was bin or our blow from the tough given that the initial temperature is a room temperature Which is 22°C and the initial height of the glass. Yes, 10 cm in the initial height of the oil inside the glasses. 9.7 cm. The volume expansion coefficient of the glass. And oils. Also given with the value of for the glass 2.7 times 10 leads to negative five per degree sell shoes. And for the oil It is 6.8 times Ben. It's a negative for their degree sand shoes. Now the oil will over blue if the change in volume of oil is equals to this this is the sum of change in volume of glass plus the difference of the initial height of glass in the oil multiplied by the cross sectional area of the cup. This is so we will use the formula for volume expansion. To solve this problem, let's start with the glass then the change in volume english equals two initial volume of blood, multiplied by the volume expansion coefficient. Andy and they're changing and very sure since we know that for a cylinder volume it's equals two area, multiplied by the hi then we have area after course, sexual area of the crop multiplied baby initial height of the cup. Multiplied by this too. It is. So this is not our Formula 40 volume off changing volume of the glass. Now for the oil then change involvement oil equals to this quantities. Equating this equation in this equation to this equation we have. Yeah. Okay. Such as. Yeah, simplifying. Mhm. Okay. And isolating the change in temperature to the left side of creation. Since this is what we're looking for and our equation becomes changing temperature, it's equals two. This okay. Yeah. Yeah. Mhm. Yeah. Now inserting me given values we have. Mhm. We know that initial height of classes 10 and the initial height of oil is 9.7. Then Their difference is 0.3 cm 9.7 cm. multiplied by expansion coefficient toward the oil just to cheese 6.8 times 10 with two negative corporate visa shoes. My honesty. I want to be height of initial height of the glass. Multiplied by its volume expansion coefficient. And solving Then the change in temperature is equals two. 40 7.43 Sell Shoes. We know that. The formula for changing bank architecture. Yes. Final 10 or 60 to minus 31 as such. T two equals two. Change in 10 plus the one so 47.4° plus 22. The grease. The answer is 69.4°. Such the olive oil will start to overflow if their final temperature is 69.4 degrees. Sure

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