Question

J (Joule’s mechanical equivalent of heat) is equal to
A) 2400 J
B) $4.18\,{\text{J/cal}}$
C) $2.2\,\,{\text{J/cal}}$
D) 1000 J

Answer 1

The Joule’s mechanical equivalent of heat is defined as the amount of work that must be done in the form of mechanical energy on a system to produce heat energy. It is defined as the ratio of the work done on the system and heat energy generated by the system.

Complete step by step answer:
The term mechanical equivalent of heat suggests that the mechanical equivalent of energy, motion, and heat energy associated with Joules are mutually interchangeable. This implies that for some systems, work and heat energy can be converted into each other and we can provide one kind of energy to make the system do work in another form. For example, we can use heat energy generated by steam to power a turbine which is in the form of mechanical energy.
The mechanical equivalent of heat is the ratio of the mechanical work done by a system to the heat supplied to the system. The number of units of work or energy equals one unit of heat, as $4.1858$, which equals one small calorie and is the classical definition of the mechanical equivalent of heat.

Hence the correct choice is option (B).

Note: In practical scenarios, there is always some energy loss while converting from mechanical to heat energy or vice versa. Joule’s mechanical equivalent of heat is a dimensionless constant which tells us the amount of work that can be done by providing heat energy to the system. Since it is a dimensionless term, we can eliminate options (A) and (D) directly since they have dimensions of energy/work done.