Question

State the first law of thermodynamics. Write the mathematical expression for it.

Answer 1

We are asked two things in this question. One is to state the first law of thermodynamics and second is to write the mathematical expression for it. We can start to attempt this question by stating the first law of thermodynamics. Then we will be able to come up with the mathematical expression of the law from the law itself. Then we can see which quantity is defined in the first law of thermodynamics.

Formulas used:
The formula derived from the first law of thermodynamics is given by,
$\Delta Q = \Delta U + W$
Where $\Delta U$ is the difference in the internal energy, $W$ is the work done by the system on the surrounding and $\Delta Q$ is the heat supplied to the system by the surrounding.

Complete step by step answer:
Let us start by stating the first law of thermodynamics. The first law of thermodynamics states that “total energy of a closed system is constant. Energy can neither be created nor destroyed. It can be transformed from one form of energy to another”. This law is also called the law of conservation of energy.

From the statement of the law, we can conclude that the heat given to the system by the surroundings is equal to the internal energy change and the work done by the system.Hence, we get the expression $\Delta Q = \Delta U + W$. Now from this we can see that this law defines the quantity of heat supplied to the system.

Note: The first law of thermodynamics is very important because it gives us an idea about the energy of a closed system. The said law is also known as the law of conservation of energy. The foundation of thermodynamics is considered to be from this law because thermodynamics is that branch of science which deals essentially with the energy and work done in a system.