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A $45-$ galuminum spoon (specific heat 0.88 $\mathrm{C} )$ at $24^{\circ} \mathrm{C}$ is placed in 180 $\mathrm{mL}(180 \mathrm{g})$ of coffee at $85^{\circ} \mathrm{C}$ and the temperature of the two become equal.(a) What is the final temperature when the two become equal? Assume that coffee has the same specific heat as water.(b) The first time a student solved this problem she got an answer of $88^{\circ}$ C. Explain why this is clearly an incorrect answer.
Because it is higher than both initial temperatures.
01:16
Aadit S.
Chemistry 101
Chapter 5
Thermochemistry
Carleton College
Brown University
University of Toronto
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We're going to take a 45 g aluminum spoon And place it in a cup of coffee at 85°C.. What is the temperature once the to become equal? So e heat of the spoon is equal to or plus the heat of the coffee. Yeah. Let's be equal to zero or he did a coffee. Take the minus the heat of the spoon. Mhm. Yeah. So mouse coffee. He capacity coffee delta. T. The coffee is people the minus mm spoon capacity spoon, delta. T. For the spoon. Institute of Values. In here the coffee is 180 grounds. You can skip the coffee. We assume the hoppy is mostly water Is 4.184. Yeah. Mhm tools per gram degrees Celsius, delta. T. Here Final temperature minus copies initially 85°C minus the mass of the spoon, 45.0 g. The capacity of the aluminum .88 tools per ground degrees Celsius. And this will be T. F minus the spoon is literally at 24 degrees Celsius, Solving for the final temperature of the mixture. Here we find that it is equal to 81.95°C for part B. The first time the students solve the problem, she got an answer. 88°C.. Explain why this is clearly an incorrect answer. So since the temperature of this food. Yeah. Mhm. Mhm. Is 24°C and that coffee, yeah is 85°C.. The temperature at which there will equilibrium is achieved. Mhm. Mhm. Mhm. Must be between, yeah, 24°C And 85°C.. Therefore the temperature of the spoon. I noticed the temperature of the mixture. Yeah. Mhm. The the mixture for the the spoon and the coffee cannot be 88 degrees Celsius. As this temperature is higher than the starting temperature. Mhm. Yeah. Yeah. Mhm mm. Yeah. Yeah. With is not possible. Mhm.
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