Question

The dimensional formula of heat is________.

Answer 1

Hint: Dimensional formula of heat is the same as energy and work. Dimensions of a physical quantity are the power to which that fundamental unit is raised to obtain one unit of that quantity. Heat energy \[Q = m \times c \times \vartriangle t\]

Complete step by step solution:
Heat is the form of energy that causes the temperature difference between the two bodies. If two bodies that are at different temperature levels are brought together, then the heat is transferred from a hotter body to a cooler body, and this is known as the transfer of heat. In solid bodies heat is transferred between two bodies by the process of conduction, for a liquid method of transfer of heat is called convection and if two bodies which are kept at a long distance then the heat is transferred in the form of radiation. This method is used in solar panels and solar cookers.

Unit of heat is Joule (J) in the International System of Units (SI) and Calorie according to the British Thermal Units. The standard unit for rate of transfer of heat transferred is given as Watt (W), joule per second.

Since heat is a form of energy so the dimensions for all form of energy will be same hence we can say dimension of heat is same as the dimension of work done, where \[work{\text{ }}done{\text{ }} = {\text{ }}force \times displacement\] and, \[force = {\text{ }}mass \times acceleration\]
\[
  Force = mass \times acceleration \\
   = \left( {{M^1}} \right)\left( {{L^1}{T^{ - 2}}} \right) \\
   = \left[ {{M^1}{L^1}{T^{ - 2}}} \right] \\
\]
Hence energy will be:
\[
  E = Force \times displacement \\
   = \left[ {{M^1}{L^1}{T^{ - 2}}} \right]\left[ {{L^1}} \right] \\
   = \left[ {{M^1}{L^2}{T^{ - 2}}} \right] \\
\]

So the dimension of heat is \[\left[ {{M^1}{L^2}{T^{ - 2}}} \right]\]

Note: Please note that while writing the dimensional formula only and only SI units of the measuring quantities should be used and should be bifurcated further.