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# Math Problems: Heat and Thermodynamics

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1. You have a 16 oz cup of coffee at 180 degrees F. That is way too hot to drink. So you want to cool the coffee off and decide to add some cold water. You add 2 ounces of cold water at 40 degrees F. How much will the water you added heat up? How much will the coffee that you poured the water into cool down?

2. An air bubble at the bottom of a lake has a volume of 15 cm3. The lake is 40 m deep and has a temperature of 4 ºC at the bottom. The bubble then rises to the surface where the temperature is 23 ºC. What is the volume of the bubble just before it reaches the surface?

3. You are sitting behind a curtain watching meters that measure pressure, volume, and temperature of some kind of heat engine. Pressure, volume, and temperature have reached an equilibrium state. Then someone behind the curtain tells you that they are going to add energy to the system. The energy is added and the equilibrium changes. Can you tell whether they did work on the system, heated the system, or a combination of both? Explain your answer.

4. In a refrigerator, heat is transferred from a colder area (the inside of the refrigerator) to a warmer area (the air outside of the refrigerator). Given what you know about internal energy, explain how this is possible.