Formula for Internal Energy to Learn in Thermodynamics

Get started with the internal energy formula to clarify all upcoming concepts and calculations in Thermodynamics. Master the sign conventions for its terms and learn to apply them to all tricky exam questions. 

The internal energy formula is ΔU = q + w. It applies universally. But its terms (q and w) depend on whether the system is open, closed, or isolated. 

In chemical thermodynamics Class 11, you learn this mathematical equation from the First Law of Thermodynamics. It measures how the energy changes (ΔU) between the initial (U_i) and final (U_f) states, and proves that the energy in an isolated system remains constant (ΔU = 0) when there is no exchange of heat (q = 0)  and work (w = 0). 

Also, unlike in physics, the sign convention in this equation is a little different in chemistry that follows IUPAC norms. We look at the heat (q) that goes into the system and the work done (w) on the system as positive when considering the formula for internal energy for chemical thermodynamics. 

Internal Energy Thermodynamics: A Brief Definition 

Internal energy is the total energy present inside a thermodynamic system. It tells us the behaviour of atoms and molecules, in terms of their kinetic and potential energies as they move and interact randomly, even when there are forces and chemical bonds among the molecules. 

We denote internal energy in thermodynamics using the letter U. But we cannot leave this symbol, as it represents internal energy to be at absolute value. And that isn’t possible. 

For different substances, the U varies. So what matters is measuring the change in internal energy between initial (U_i) and final (U_f) states. Be it, before and after heating, or before and after a chemical reaction. 

To denote this change in internal energy, we use ΔU, which equals (U_f - U_i). That tells us that internal energy is a state function, which only considers first and last phases. That is, not the path taken. This is the first part of the formula for internal energy. 

Formula for Internal Energy in Thermodynamics Explained

Let’s do a deep dive into the internal energy formula here. 

Sources that Lead to Internal Energy Change

Ask yourself what could lead to a change in internal energy. 

There are three conditions or factors, also highlighted in NCERT Chemistry Chapter 5 Thermodynamics, which tell us that internal energy can change. 

1. Heat (q) is supplied to the system from the surroundings, or it passes out of the system to its surroundings
2. Work (w) is done on the system. Work (w) can also be done by the system.
3. If the system remains open or closed, matter can enter or leave.    

First Law of Thermodynamics Proves the Internal Energy Formula

So, how is the First Law of Thermodynamics in Chemistry related to the change in internal energy?

The first law of thermodynamics states energy cannot be created or destroyed. It can only change its form. So the total energy of an isolated system or the universe will be constant. 

For any process in a thermodynamic system, we have a system that can only gain or lose energy when heat and/or work are exchanged with the surroundings. 

Now, since we are concerned with work done and heat exchanged in a system, we can use the First Law of Thermodynamics to calculate the change in internal energy. 

The general change in internal energy equation following the first law is

ΔU = q + w 

With this formula for internal energy, we can track any energy change in the thermodynamic process. And likewise, prove that energy is always conserved. 

Sign Conventions in the Internal Energy Change Formula

It is important to understand the sign conventions while using the internal energy change formula. 

Heat (q) sign convention

1. +q: This will be a positive sign when heat enters the system from its surroundings. That also means that there will be an increase in internal energy.
2. -q: When heat leaves the system into the surroundings, there will be a decrease in internal energy. The heat will have a negative sign then. 

Work (w) sign convention

1. +w: This is positive work when work is done on the system by the surroundings. That will increase internal energy.
2. -w: When work is done by the system on the surroundings, it will be in a negative sign. That shows there is a decrease in internal energy. 

Things to note on the sign conventions for Internal Energy Change

• If heat is positive, energy enters the system. While, if it’s negative, it means energy leaves. 
• When work is positive, energy is put into the system. But if it’s negative, the system uses energy to perform work on its surroundings. 

Remembering the Internal Energy Formula for Class 11 Chemistry

The internal energy formula is the mathematical equivalent of the First Law of Thermodynamics. It opens doors to understanding the different applications of thermodynamics in Chemistry, which include enthalpy, entropy, and all other calculations in thermodynamics. 

Test your waters with Class 11 Thermodynamics NCERT Solutions next!