# Turning Work into Thermal Energy in Joule’s Experiment

In Joule’s famous experiment where he determined the specific heat capacity of water, he used a paddle to increase the temperature of the water. That is, the kinetic energy of the paddle went into the thermal energy of the water. My question is exactly how did the paddle’s kinetic energy become the water’s thermal energy? Was it because

1. The paddle experienced resistive forces in the fluid that dissipated its energy, much the same way friction converts mechanical energy into thermal energy?
2. The paddle exerted a force on the fluid particles that caused them to move in the same rotational motion as the paddle, thus imparting kinetic energy to them (i.e. increased internal energy)?

The kinetic energy of the paddle didn't really change. Its rotational speed was constant. There was viscous dissipation (analogous to the action of a viscous damper) taking place within the fluid that converted the work done by the paddle into internal energy.

• So the answer to my question would be the first option? Why can’t the second option be true? Apr 5, 2016 at 11:45
• With regard to the first one, I usually don't think of viscous stresses and viscous dissipation as friction because they occur throughout the fluid, and not just at the surface of the paddle. With regard to the second one, the transport of momentum by viscous stresses involves exchange of momentum between slower moving- and faster moving particles throughout the fluid. If that is what you meant, then, yes, this is correct. For a detailed quantitative discussion of viscous momentum transport, see Transport Phenomena by Bird, et al. Apr 5, 2016 at 11:51
• @lightweaver The paddle wants to slow down, because the energy of the paddle is being absorbed by the water, initially in the form of movement, but later in the form of temperature gain, because the movement itself is turbulent and is met with friction internally and with the glass. If you could somehow get water to rotate without friction on the glass or internal friction caused by turbulence, it would never stop rotating, and the temperature would not rise.
– Neil
Apr 5, 2016 at 12:18
• @Neil Turbulence is not required for viscous heating to occur. Viscous heating also occurs in laminar flows, particularly for highly viscous fluids. Apr 5, 2016 at 12:54

There is no either-or between your two answers. These are two aspects of the same.

By Newtons "actio=reactio", that a force is working on the paddle is equivalent to that the paddle acts with a force on the water. The energy lost by the paddle is gained by the water. If there is a constant driving force on the paddle, then the paddle gets the same amount of energy that it lost to the water back from the driving force.

In a multiple choice test I'd rather take your second option, though, because the first formulation is worse. I would call "dissipation" the act of converting kinetic energy into heat. And this will take place mostly after the interaction of the paddle and the water: first, the water is set in motion, then it gets slowed down by internal friction and heats up.