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# Thermal Properties of Internal Energy

Aug 27, 2022

### Key Concepts

• Internal energy
• Change in internal energy
• Work
• Heat

### Introduction:

In this session we will be looking at change in internal energy of a system of particles, explore it further and discuss about it.

### Explanation:

Internal energy:

A system of particles may posses many different kinds of energies such as,

1. Kinetic energy of the randomly moving particles.
1. Potential energy due to the interaction between the particles.
1. Chemical energy due to the chemical bonds in the particles (if any).
1. Electrical energy of the atoms and molecules (particles).

And many more.

Internal energy, U is the total energy of a system. That is associated with random, disordered motion of molecules. It includes the kinetic energy, potential energy, chemical energy, Electrostatic energy etc. of the system.

The Law of conservation of energy is the foundation of the First Law of thermodynamics. Law of conservation of energy states that the internal energy of an isolated system remains constant. Thermodynamics is not concerned about calculating the internal energy of a system. However, it is more important to observe the change in internal energy (ΔU) of a system.

### Change in internal energy:

Internal energy of a system may change in many ways such as,

1. Internal energy increases: When energy is added to a system, its internal energy increases, +ΔU. This also increases the temperature of the system, +ΔT
1. Internal energy decreases: When energy is removed from the system, its internal energy decreases, ΔU. This also decreases the temperature of the system, ΔT
1. Isothermal process: In such case ΔT = 0. Thus, there is no change in the internal energy of the system, ΔU = 0.

The internal energy of the system increases when its temperature increases and vice-versa. It changes when energy is transmitted into or out of the system by the following means:

1. Work (movement of the piston)
1. Heat (heating/cooling of the system)

Both of them have the same unit of measurement i.e., Joules. Either way, the internal energy of a gas system can be increased or decreased.

## Work:

Work is a macroscopic/visible transfer of energy into or out of a system.

It is a mechanical way to add or remove energy from a gas system which involves the physical movement of the piston.

The force that moves the piston is due to the pressure acting on the inside and the outside areas of the piston.

### Case 1 : Work done on the gas:

Pressure inside > Pressure outside

¯

Piston moves inwards.

¯

Work is done on the gas.

¯

The volume of the gas decreases.

¯

The internal energy of the system increases, as the environment adds energy to the system.

### Case 2: Work done by the gas:

Pressure inside < Pressure outside

¯

Piston moves outwards.

¯

Work is done by the gas.

¯

The volume of the gas increases.

¯

The internal energy of the system decreases, as the gas uses its energy to push the piston outwards

### Case 3: Isochoric process (DV = O)

Pressure inside = Pressure outside

¯

Piston does not move.

¯

No work is done (W = O)

¯

The volume of the gas does not change (DV = O)

¯

The internal energy of the system remains the same.

## Heat:

Heat is a microscopic/invisible transfer of energy into or out of a system. Heat can be added or removed by touching a reservoir (air or water around it) to the system. The energy transferred into or out of the reservoir is negligible compared to its huge size. Therefore, they have a constant temperature and transfer heat at a constant rate. A hot/cold reservoir has a temperature greater/smaller than the system.

Total change in internal energy:

The total change in internal energy of a system is the sum of the change in internal energy due to work done (W) and heat transferred (Q).

ΔU = W + Q

The work done (W) and heat transferred (Q) are taken to be positive/negative when they add/subtract internal energy to/from the system.

1. During a thermodynamic process, 350 joules of heat are added to a gas while 200 joules of work are done by the gas. Determine the change in internal energy.

Given that,

Heat = 350 J

Work = – 200 J (when the work is done by the gas, it decreases the internal energy of the system, so it is taken as negative)

Total change in internal energy, ΔU = W + Q

ΔU = – 200 + 350

ΔU = 150 J

Thus, the change in internal energy is 150 J.

1. During an isothermal process 120 J of heat are removed from a trapped gas. Find out the change in internal energy of the system. Is the work done on or by the gas?

Given that,

Heat = – 120 J (Heat is removed)

Isothermal process means ΔT = 0

As the temperature of the system does not change at all, the internal energy of the system remains constant.

Thus, ΔU = 0

Here, ΔU = 0 = Q + W

0 = (-120 J) + W

W = 120 J

A positive work done indicates that the work is done on the gas

### Summary

• Internal energy, U is the total energy of a system. It includes the kinetic energy, potential energy, chemical energy, Electrostatic energy etc. of the system.
• The internal energy of a system increases with an increase or decreases with a decrease in temperature of the system.
• Work and heat are the two processes by which the energy can be transferred in and out of the system.
• The internal energy of a system increases when the work is done on the system and it decreases when the work is done by the system.
• The internal energy of a system increases when the heat is added to the system and it decreases when the heat is taken out of the system.

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