Question

Dimensional formula of $\Delta Q$, heat supplied to the system is:

Answer 1

In this question, first we will study the basics of heat energy. This will help us to get the required answer. Further, we will discuss the basic concept of energy and the law of conservation of energy, for our better understanding.
Formula used:
$\Delta Q = m \times C \times \Delta T$

Complete step by step solution:
As we know, the heat supplied to a system is in the form of heat. Also, we can say that heat is the form of energy that is transferred between two or more systems, with different temperatures. We know that heat is transferred from the high-temperature system or body to a low-temperature system or body.
Mathematically heat supplied to any system is given by:
$\Delta Q = m \times C \times \Delta T$
Here, m is the mass of the system or body, C is the specific heat capacity of the system or body, T is the change in temperature of the system or body.
Further, heat is also known as heat energy or thermal energy. It is measured in Btu or calories or joules.
Here, as we know the fundamental dimension formula is given by mass M, length L and time T:
$\left[ {{M^0}{L^0}{T^0}} \right]$
So the dimensional formula of heat(energy) is given by:
$\left[ {M{L^2}{T^{ - 2}}} \right]$ (This is form of energy so dimensional formula will also be equivalent to energy)
Therefore, we get the required answer.
Additional information: As we know that the energy can be defined as the ability to do work by any object or body. Also, energy can be found in many different things and energy can be converted in different forms, for example-kinetic energy is the energy of motion of an object or body, and potential energy is energy produced due to an object's position. We also know that the total energy of a system is always given by the sum of its kinetic energy and the potential energy.
We also know from the law of conservation of energy, which states that energy can neither be created nor be destroyed; rather energy can only be transferred from one form to another form.
We should also know about the term power. Power is the amount of energy that is transferred or converted by the object or boy per unit time. Also, the International System of power is given in watt. Here, power is a scalar quantity, which means that power has only magnitude but not direction.

Note: We should remember that the dimensional formula is given by mass, length and time only. Also, the laws of conservation of energy can never be violated in any case. According to the law of conservation of energy, energy can neither be created nor be destroyed; rather it can only be transferred from one form to another.