Question

I have a body on a horizontal surface with friction. My thermodynamics system is only the body and I want to describe this with the first law of Thermodynamics. Suppose the body has a start kinetic energy and for the friction in the final state it has no more kinetic energy. For this problem there isn't a heat exchange but only a work exchange caused from the friction. How can i write the fist law with this system?

Answer 1

The first law of thermodynamics for an isolated system with no heat exchange and only work exchange due to friction can be simplified to ΔU = W. Since there is no heat transfer (Q=0), the work done by friction on the body is equal to the negative of the body's initial kinetic energy.

Step-by-step explanation:

The student is asking about the application of the first law of thermodynamics to a situation where a body on a horizontal surface comes to rest due to friction. Since the system is isolated and there is no heat exchange (Q=0), the first law simplifies to the change in internal energy (ΔU) being equal to the net work done by the system. With the body slowing down due to friction, kinetic energy is converted into internal energy.

The first law of thermodynamics in this case can be written as:

ΔU = W

Since there is no heat exchange, Q is zero, and therefore the work done by friction (W) is equal to the negative of the initial kinetic energy of the body because it's losing that energy as it slows down. Mathematically, if the initial kinetic energy is Ki and final kinetic energy Kf is zero, the work done by friction is W = Kf - Ki = -Ki. As a result, the increase in internal energy is equal to the initial kinetic energy that the body had, which is now dissipated as heat due to friction—despite no heat being transferred into or out of the body.