Internal Energy Formula

Internal energy refers to the amount of energy required to bring the system from its standard internal state to its present internal state. It is the energy contained within the system.

• Internal energy formula is the sum of kinetic and potential energy relative to the centre of the mass of the system.
• It is possessed by the system due to molecular motion and molecular configuration. 
• The molecular motion is kinetic energy, whereas the molecular configuration is Internal potential energy.
• It is associated with the random motion of the particles that are used for the preparation of a substance. 
• Internal energy is expressed in the law of conservation of energy, which is the foundation of the first law of thermodynamics.
• It can be represented as:

ΔU=Q−W

• Where, W is the work done by the system
• Q is the heat exchanged between a system and its surroundings.
• U is the total internal energy of the system.

Key Terms: Internal Energy, Internal Energy Formula, First Law of Thermodynamics, Law of Conservation of Energy, Chemical Energy, Kinetic Energy, Potential energy

---

What is Internal Energy in Thermodynamics?

[Click Here for Sample Questions]

Internal energy is the microscopic energy contained within a system formed by the disordered movement of molecules (kinetic energy), potential energy, and the nuclear energy present within the atoms of these molecules. 

• It is responsible for gains and losses of energy due to changes in its internal state.
• The internal energy is denoted by ‘U’ and is measured in joules (J). 
• This energy can increase with the increase in temperature and change of state or phase (from solid to liquid to gas). 
• Heat reservoirs store this energy.
• Different substances will have different internal energies depending on the atom, temperature, bonds, pressure, etc.
• It is a state variable and a thermodynamic potential that depends only on the internal state of the system.

Also Read:

---

Internal Energy Formula

[Click Here for Sample Questions]

The internal energy formula is derived from the first law of thermodynamics, which simply explains that the internal energy of the system cannot be changed and is constant.

• So, according to the first law of thermodynamics, internal energy is given as

ΔU = Q - W

• It can also be rewritten as ΔU = Q - PV (since W is PV).
• Where, W is the work done by the system
• Q is the heat exchanged between a system and its surroundings.
• U is the total internal energy of the system.

Change in Internal Energy

Change in Internal Energy can be defined as the sum of work done by the system and the heat exchanged between a system and its surroundings.

• Mathematically, it can be expressed as

ΔU = E_B – E_A

• where E_A and E_B are the energies in states A and B

Internal Energy at Constant Pressure

The internal energy at constant pressure is given as

ΔU = Q – ΔV

• Where, W is the work done by the system
• Q is the heat exchanged between a system and its surrounding.
• V is the change in volume of a system.

The internal energy for different gases are as follows:

 Internal Energy

---

Things to Remember

• Internal Energy is the sum of all energies present in a system.
• It contains all forms of energy that include translational energy, rotational energy, vibrational energy, and nuclear energy.
• Internal Energy of gas and solid/liquid is given as Δ U = mc_vT and ΔU = mc_vΔT respectively.
• The first law of thermodynamics states that the change in total energy is equal to the difference between heat added to the system and work done by the system.
• Kinetic energy is the energy possessed by the body by virtue of its motion.
• Potential energy is the energy possessed by the body by virtue of its position.

Also Read: