A 5.8-kg box having an initial speed of 4.0 m/s slides along a rough table and comes to rest. Estimate the total change in entropy of the universe. Assume all objects are at room temperature (293 K).
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This is Giancoli answers with Mr. Dychko. The change in entropy of the universe is gonna be the amount of heat added to the universe divided by the universe's temperature and the amount of heat that it gains is going to be equal to the amount of kinetic energy that's been lost from this box. So all the kinetic energy of the box once had is going to get turned into heat and so that's going to be the final kinetic energy minus the initial kinetic energy and, and the final kinetic energy zero because it comes to arrest and I put these absolute value signs here just to say that this is take the positive of this. It's going to end up being a negative number because it's lost kinetic energy. But in terms of the amount of heat added to the universe the number is going to be positive because it's whatever is lost in kinetic energy is gained as, as heat. So we have one-half times mass times the speed squared and that's one-half times 5.8 kilograms times four meters per second squared divided by the temperature in Kelvin of 293 Kelvin. And that gives 0.16 Joules per Kelvin change in entropy of the universe.
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