The mechanical equivalent of heat is a concept that relates mechanical work to heat energy. It's represented by the letter "J" and has a numerical value of approximately 4.184 joules per calorie.

Since it represents a conversion factor between units of work (joules) and units of heat (calories), its dimensional formula is simply dimensionless.

Here's why:

* Work: [M L² T⁻²] (mass * length² * time⁻²)

* Heat: [M L² T⁻²] (same dimensions as work)

When you divide work (in joules) by heat (in calories), the units cancel out, leaving you with a dimensionless quantity.

Therefore, the dimensional formula for the mechanical equivalent of heat is [M⁰ L⁰ T⁰], which is equivalent to 1.