Angle is defined as the ratio of length of arc to radius.

Mathematically,

Angle = Length of Arc / Radius

Dimensional formula of Length = M⁰L¹T⁰
Dimensional formula of Radius = M⁰L¹T⁰

Substituting in the above formula we get,
Dimensional formula of Angle = M⁰L⁰T⁰. We can also say Angle is dimensionless quantity.
SI unit of Angle is radian (rad)

Mechanical equivalent of heat can be defined as the amount of work done to produce a unit quantity of heat. In other words whenever a mechanical work is completely transformed into heat, the amount of heat produced is directly proportional to the amount of work done.

W ∝ Q  —— Where W = Amount of Work and Q = units of heat.
W = J Q

In the above equation constant J is Known as Mechanical equivalent of heat or Joule’s equivalent.
From above equation we get,

Mechanical equivalent of heat (J) = Amount of Work (W) / units of Heat (Q).

Dimensional Formula of Work = M¹L²T^-2
Dimensional Formula of Heat = M¹L²T^-2

substituting these values we get,

Dimensional Formula of Mechanical equivalent of heat (J) = M⁰L⁰T^-0 . we can also say Mechanical equivalent of heat (J) is dimensionless quantity.
SI unit of Mechanical equivalent of heat (J) is Joules/calorie (J calorie^-1 ).

Internal energy (U) is defined as the energy which is related to atomic, sub atomic and molecular energy of the system. Internal energy comprises of the kinetic and potential energy related with transitional , rotational and vibrational motion of the molecules, it also includes the energy of electromagnetic interactions of molecules , atomic and sub atomic constituents of molecules.

Mathematically,
Internal energy (U) = Energy.
Dimensional formula of Energy = M¹L²T^-2

So Dimensional Formula of Internal Energy (U) = M¹L²T^-2
SI unit of Internal Energy (U) is Joule (J)

Specific heat capacity is defined as the quantity of heat required to increase the temperature of a unit mass of fluid by one temperature unit.

Mathematically,
Specific heat capacity = Q /m Θ

Where Q= Heat, m = mass  and Θ = Temperature

Dimensional formula of Heat(Q) = M¹L²T^-2
Dimensional formula of mass = M¹L⁰T⁰
Dimensional formula of Temperature(Θ) = M⁰L⁰T⁰K¹

Putting these values in above equation we get,
Dimensional formula of Specific Heat Capacity = M⁰L²T^-2K^-1
SI unit of Specific Heat Capacity is Joule kg-1 K^-1

1. When we write a unit in full, the first letter should not be in capital.
Example: metre and not as Metre kilogram and not as Kilogram

2. Name of scientist as the symbols of unit should be in upper case (capital) letter
Example: N for newton, J for joule.

3. The singular form of the unit should be used.
Example: km and not as kms, Kg and not as kgs

4. At the end of the abbreviations there should be no full stop.
Example: mm and not as mm, kg and not as kg.

5. The degree sign is omittedwhen temperature is expressed in Kelvin.
Example: 273K not as 2730 K

6. Accepted symbols should only be used.
Example: ampere is represented as ‘A’ and not ‘amp’
second is represented as ‘s’ and not ‘sec’

7. Not more than one solidus or slash should be employed. But effort should be made to avoid use of solidus or slash.
Example: J/k.mol or Jk.mol^-1 but not J/k/mol
J kg^-1K^-1 but not J/kg/K

8. Between the number and the symbol of the unit, one letter space is always to be left.
Example: 2.3 m and not as 2.3m
Kg m s^-1 and not kg ms^-1

9. A physical quantity in numerical value should be expressed as p= a × 10m
Here ‘a’ is a number between 1 and 10 and ‘m’ is the appropriate power of 10.
Example: velocity of light c = 2.997 × 10 ms^-1 .