Question

The mechanical equivalent of heat
A. Has the same dimension formula as heat
B. Has the same dimension formula as work
C. Has the same dimension formula as energy
D. Is dimensionless

Answer 1

Hint: In order to answer the question, one must be aware of the term ‘mechanical equivalent of heat’. This question can be done by the option elimination method as follows: we know that the dimensions of heat, work and energy are the same. So, if the question is single option correct type then option D is the correct answer. Since, option A, B and C, all three cannot be correct in case of single choice questions.

Complete step by step answer:
First, let us understand what the term, ‘mechanical equivalent of heat’ is. The mechanical equivalent of heat suggests that the motion and heat are mutually interchangeable when the work done is totally converted into heat energy. This means that for some systems, work done will be converted into heat energy and providing heat energy will do the equivalent amount of work without any loss.
Now, the mechanical equivalent of heat is calculated by taking the ratio of work done and heat energy.
Since we have already discussed above that the SI units of work done and heat energy are the same. Therefore, the ratio of work done and heat energy will be a dimensionless quantity.

Hence, option D is the correct option.

Note: It must be noted here that in practical life, there is always some heat loss to the system. There may be many factors responsible for this including friction between two objects. Mechanical equivalent of heat will be a numerical value with no dimension. The implication of mechanical equivalence of heat is that one can change the internal energy of the system by either doing work to the system, or adding heat to the system.