A 4.0-kilogram wood block starts with an initial speed of 9.0 meters per second and slides across the floor until friction stops it. What is the approximate change in entropy of the universe? Assume that everything stays at a room temperature of 25 degrees Celsius.
In this scenario, we’re told of a wooden block of a given mass and initial speed which due to friction eventually comes to rest after sliding across a floor. We want to know the approximate change in entropy in the universe due to this process, what we can call Δ𝑠. Recalling that a mathematical definition for change in entropy is that it equals the heat added to a system divided by the temperature of that system.
In our case, the heat added to the system is due to the friction between the floor and the block. And we can quantify that heat energy in terms of the change in energy of the block as it comes to a stop. With Δ𝑠 being equal to the heat energy provided divided by the temperature of our object, we can say that that heat energy is equal to the change in kinetic energy of our mass. That is, one half its mass times its initial speed squared.
This means then that the change in entropy in our system, and therefore in the universe, is equal to the mass of the block times its initial speed squared over two times the temperature of everything in the room. That mass, we’re told, is 4.0 kilograms. And that initial speed is 9.0 meters per second.
When we go to plug in for our temperature, instead of simply plugging in 25 for degrees Celsius, we convert this temperature into Kelvin scale by adding 273.15 to it. This is temperature measured on the absolute temperature scale which fits our calculation. We find that Δ𝑠 is 0.54 joules per Kelvin. That’s the approximate change in entropy, an increase in entropy, in the universe due to this sliding process.