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Heat and Thermodynamics

1. You take a 50 g glass coffee mug from the dishwasher following the dry cycle. You use a dishcloth because the temperature of the mug is 90 deg C. You fill the mug with 250 g of cold water from the refrigerator. The temperature of the water is 5 deg C. Assuming that no heat is lost to either the air, the kitchen counter, or to your hand (all stupid assumptions, but what the heck), what will be the final temperature of the cup, and of the water in it? [Specific heats: glass, 837 J / (kg)(C); water, 4186 J / (kg)(C) ]

2. A spacecraft power system generates electricity by absorbing heat from a nuclear reactor operating at 1000 deg C and expelling heat from a radiator operating at 300 deg C. What is the theoretical maximum efficiency of the system? (Don't forget, temperatures must be in K, not C!)

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1. Let the final equilibrium temperature of the cup and water be T.

As we assume no heat is lost to the surroundings, heat lost by the cup in cooling down from 90 degrees C to T must go to the water to heat it up from 5 degrees C to T.

Heat lost by ...

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