Question

The dimensional formula for entropy is
A. $[ML{T^{ - 2}}{K^1}]$
B. $[M{L^0}{T^{ - 2}}]$
C. $[M{L^2}{T^{ - 2}}{K^{ - 1}}]$
D. $[M{L^2}{T^{ - 2}}K]$

Answer 1

You can start by briefly explaining distance and speed. Then write the equation for speed, i.e. $s = \dfrac{d}{t}$ . Then apply this equation for the first half of travel, the second half of the travel and then for the overall travel and obtain the time taken in each case. We know that the time taken for the overall travel will be equal to the sum of the time taken for the first and second half of the travel. Use this relation to reach the solution.

Complete step by step answer:
You can start by explaining dimensional formula, heat, temperature and entropy. Remember to mention the dimensional formula of heat and temperature. Then use the equation from the second law of thermodynamics, i.e. $\Delta S = \dfrac{{\Delta Q}}{T}$ and place the dimensional formula of heat and temperature to reach the solution.
Before attempting the mathematical calculations let’s first look at some important concepts
Dimensional formula – Every physical quantity has a unit assigned for it, for example force has a unit $kgm/{s^2}$ . When we express this unit in terms of the fundamental quantities we get the dimensional formula of that physical quantity. The dimensional formula for force is $[ML{T^{ - 2}}{K^0}]$.
Here $M$ represents mass, $L$ represents length, $T$ represents time and $K$ represents temperature.
Heat – It can be more simply understood as heat transfer. It is the measurement of the thermal energy that is transferred when a system having a certain specific heat and mass undergoes a temperature change. Its dimensional formula is $[M{L^2}{T^{ - 2}}{K^0}]$ .
Temperature – It is a physical quantity that determines how hot or cold an object is. It is an intensive property (a property that depends on the quantity of matter in the system). The dimensional formula of temperature is $[{M^0}{L^0}{T^0}{K^1}]$ .
Entropy – Entropy in thermodynamics is defined as an extensive property (a property that depends on the quantity of matter in the system) which determines all the possible configuration a system can have. It is also the measure of the energy that is not available for doing work.
According to the second law of thermodynamics the change in entropy is equal to the change in the amount of heat divided by the temperature.
$\Delta S = \dfrac{{\Delta Q}}{T}$
So the dimensional formula of entropy is equal to the dimensional formula of heat divided by the dimensional formula of temperature, i.e.
Dimensional formula of entropy $= \dfrac{{M{L^2}{T^{ - 2}}{K^0}}}{{{M^0}{L^0}{T^0}K}} = M{L^2}{T^{ - 2}}{K^{ - 1}}$

So, the correct answer is “Option C”.

Note:
As you may have noticed we calculated the dimensional formula of change in entropy rather than of entropy itself, this is done because the dimensional formula for entropy and change in entropy is the same. Additionally dimensional formulas are unique, whereas units can be measured in SI unit system, metric system, etc.