The combined molecular kinetic energies of molecules in a cool lake are greater than the combined molecular kinetic energies of molecules in a cup of hot tea. Pretend you partially immerse the teacup in the lake and that the tea ?absorbs? 10 calories from the water and becomes hotter, while the water that gives up 10 calories becomes cooler. Would this energy transfer violate the first law of thermodynamics? The second law of thermodynamics? Defend your answers.
Solution 17E STEP 1: The combined kinetic energy of the cool lake is greater than the cup of hot tea. Obviously the number of molecules is more in the lake than the tea cup. So the total kinetic energy is greater for the lake. But from statistical mechanics we know that, the average kinetic energy of a system determines the temperature of the system. So, the average kinetic energy of the cup of hot tea must be higher than the average kinetic energy of the lake. Otherwise the cup of tea would have less temperature than the lake, which is not the case here. STEP 2: As you immerse the cup partially into the lake, if the tea cup absorbs 10 cal from the lake and becomes hotter, it would not violate the 1st law of thermodynamics. The 1st law states that, dE = dQ dW -------------------(1) This tells that the change in internal energy of the system is the difference between the amount of heat added to the system and work done by the system. As the cup of tea gets 10 cal, it would increase the internal energy of the system. STEP 3: But the serious case is, without doing any external work, the cold lake became more cold and the hot tea cup became more hot. We know that, if two bodies of different temperature come into contact with each other, the hotter body will become cooler and the cooler body will become little hotter. Finally they will attain thermal equilibrium. Once they will be in equilibrium, there cannot be temperature difference again without external work done. But here the cold object became more cooler and the hot object became more hotter. This will violate the 2nd law of thermodynamics. The 2nd law tells that the entropy of the universe must be increased all the time and the entropy of the system must increase or remain constant. But in the above case, the entropy reduced without external work done on the system. So, it will violate the 2nd law.