Question

Energy equivalent to one erg, one joule, one calorie is in the order:
A. $1erg > 1joule > 1calorie$
B. $1erg > 1calorie > 1joule$
C. $1calorie > 1joule > 1erg$
D. $1joule > 1 calorie > 1erg$

Answer 1

Bring all the values to a specific unit to easily compare. This is just like making a ratio so uniform values to a single unit can give the possible outcome.

Complete step by step answer:
It is known that $1erg$ is a CGS unit and the value of$1erg$ is${10^{ - 7}}J$. This means that $1erg$ is equivalent to $100nJ$ which is the unit of nanojoules. Joule is the SI unit of energy of any system.
The second comparison is made between joule and calorie where the calorie is the unit in CGS and the Joule is the unit according to the SI system. The value of $1Calorie$ is similar to $4.184J$ which is approximately written as $4.2J$ .
Therefore, from the two comparisons it is clear that $'erg'$ is the smallest unit with respect to energy equivalence. Hence the conversion of Joule to erg will be:
$1J = {10^7}erg$
It is given that in the process of calorie conversion$1Calorie$ is $4.184J$. If the calorie needs to be converted to erg, then the conversion process will be:
$1Calorie = 4.184J$
= $4.184 \times {10^7}erg$
Therefore, if we compare the value of$1erg$, $1calorie$ and $1joule$ on the basis of their equivalent values in erg, then the results will be $1erg$, $4.184 \times {10^7}erg$ and ${10^7}erg$.
As a result, the order of values according to the energy equivalent is $1calorie > 1joule > 1erg$.

So, the correct answer is Option C.

Note: Different units while defining the ratio need to be brought to the same level. There can be more than a single CGS unit for the same physical quantity depending on the level of magnitude. This does not prove that they are equivalent to each other.