You are going to have to make many assumptions to do this calculation. First the heat Q being dumped into the diamond stylus is at the same time being dissipated by the stylus assembly to its surroundings. This will involve the temp. difference between the diamond and its surroundings, geometry of system, heat conduction coefficient, heat capacity, etc. Probably best to determine the equilibrium temp empirically. Heat dissipation calculation involves a nasty partial differential eqn. Then there is the vinyl: it is moving, constantly exposing new room temp. vinyl.
The heat dumped into the stylus will equal its dissipation at its equilibrium temp.
Presumably the rest will be dumped into the vinyl. Temperature will depend on heat capacity of the vinyl and how fast it is conducted away (that nasty heat conduction eqn. again).
Now the heat generated Q as the result of friction, as has been already mentioned, depends on the pressure, coefficient of friction and velocity. Now the linear velocity is changing do to the change in radius of the record as it plays. Then there is the stylus velocity due to the music. Now this velocity is frequency dependent (increases linearly with frequency).
So, assumptions need to be made to calculate a ballpark figure: like an average stylus velocity. I would assume that the dissipation of heat from the stylus is small and can be ignored. With that we can assume that all the heat generated is dumped into the vinyl. Heat conduction in the vinyl is probably small enough that one can assume that for an instant all the heat is contained in a small volume (but how small?). That would have to be addressed since heat capacity calculations require a mass to calculate a temp. .
So, this simple little calculation turns out to be a bit of a sticky wicket.
The heat dumped into the stylus will equal its dissipation at its equilibrium temp.
Presumably the rest will be dumped into the vinyl. Temperature will depend on heat capacity of the vinyl and how fast it is conducted away (that nasty heat conduction eqn. again).
Now the heat generated Q as the result of friction, as has been already mentioned, depends on the pressure, coefficient of friction and velocity. Now the linear velocity is changing do to the change in radius of the record as it plays. Then there is the stylus velocity due to the music. Now this velocity is frequency dependent (increases linearly with frequency).
So, assumptions need to be made to calculate a ballpark figure: like an average stylus velocity. I would assume that the dissipation of heat from the stylus is small and can be ignored. With that we can assume that all the heat generated is dumped into the vinyl. Heat conduction in the vinyl is probably small enough that one can assume that for an instant all the heat is contained in a small volume (but how small?). That would have to be addressed since heat capacity calculations require a mass to calculate a temp. .
So, this simple little calculation turns out to be a bit of a sticky wicket.