THE FIRST LAW OF THERMODYNAMICS

THE FIRST LAW OF THERMODYNAMICS

• The first law of thermodynamics was drawn from the law of conservation of energy and the thermodynamics process. It also differentiates the two kinds of transfer of energy:

• Heat
• Thermodynamics work

• One needs to understand heat, mass, and internal energy before stating the first law of thermodynamics
• The energy associated with molecules that includes kinetic energy and potential energy, is called internal energy
• There may be several transformations of energy that take place in the system when heat, work, and internal energy get changed. Throughout the entire process, the total energy remains the same
• This law tells about the different forms of heat and its causes

STATE FIRST LAW OF THERMODYNAMICS

According to the first law of thermodynamics, while doing external work, some amount of heat is given to the system. Then,

Amount of the heat absorbed = Sum of the increase in internal energy of the system

It is due to an increase in temperature, as well as the external work done by the system during the process of expansion.

∆Q Heat supply

In simple words, the first law of thermodynamics is defined as

Heat supplied to system = sum of the changes in internal energy + work done by the system

The first law of thermodynamics equation is represented by

ΔU =ΔQ – ΔW

ΔU represents a change in internal energy of the thermodynamic system

ΔQ represents heat given to the system

ΔW represents work done

If we differentiate the above equation, we get dU=dQ-dW

SIGNIFICANCE OF FIRST LAW OF THERMODYNAMICS

• The principle of the law of energy conservation is how the first law of thermodynamics is formulated. It represents energy that can be transferred from one body to another, but it cannot be created nor destroyed.
• The changes take place in the system from the initial stage to the final stages. dQ and dW changes throughout the process. However, throughout the entire process dU= dQ -dW remains the same –

U (internal energy)

At molecular level

Energy = Sum of K.E (kinetic energy) and potential energy

Here are 3 types of K.E and three types of potential energy are given below

U=translational motion(kinetic energy) + Vibrational motion(Kinetic energy) + Rotational motion(Kinetic energy) + Force of attraction of electrons and nucleus(Potential energy) + binding energy of molecules

U (internal energy) depends on the final and initial state of the system. It is independent of path.

dU = nCvΔT

where,

• n represents the number of molecules present in the body
• ΔT represents a change in temperature(small)
• Cv represents, at constant volume, the molar-specific heat capacity

Q (Heat)

If the heat is added to the system, it is positive, and if the heat is released from the system, it is negative

• At constant volume dQ= nCp ΔT
• At constant pressure dQ= nCvΔT

W (Work)

• Work done on the system is represented by a negative sign(-ve)
• Work done by the system is represented by a positive sign(+ve)

Relation: Δ U = Q − W .

DEFINE THE FIRST LAW OF THERMODYNAMICS

• The principle of the law of energy conservation is where the first law of thermodynamics is formulated. It represents energy that can be transferred from one body to another, but it can neither be created nor be destroyed
• At equilibrium, the thermodynamic process produces a state variable called internal energy
• According to the first law of thermodynamics, energy remains the same throughout the universe

To understand much better, here is an example.

Consider a heat engine that converts thermal energy to mechanical energy and vice versa. Heat engines have different types of relationships with heat, pressure, and the volume of the working fluid, which is normally a gas. Here, energy is transferred during phase changes from liquid to gas, or vice versa. In such cases, energy is not created.

• The energy remains constant in the isolated system
• Internal energy is mass-dependent(extensive property), and specific energy is independent of mass(intensive property)

FOR EXAMPLE:

1. Consider oxygen gas has a constant pressure in the system. There is a loss of 150 J of heat in the surroundings around the system. 400 J of work is done onto the system. Find the system’s internal energy of the oxygen gas?

Solution:

ΔU = Q – W

ΔU = 150J – (- 400J)

ΔU =  550J

ΔU is the internal energy relationship that revolves between the system and surroundings. If the surroundings lose some energy, the system gains the lost energy. Moreover, the surrounding area will also lose some heat to carry out work in the system.

APPLICATION OF THE FIRST LAW OF THERMODYNAMICS

Here are a few applications of the first law of thermodynamics in real life :

1. Refrigerators
2. Thermal power plants
3. Engines

If the door of the refrigerators is kept open for a long period, then the entire room’s temperature will rise.

Here are some other applications

• Isothermal process
• Melting process
• Mayer’s formula

ISOTHERMAL PROCESS

The ideal gas temperature remains the same in the case of an isothermal process (dU = 0) so that

dQ = dU + dW ⇒ dQ = dW.

MELTING PROCESS

Internal energy increases when solid melts to liquid, where m is the mass of liquid and L is the latent heat of the solid. In the system, the heat absorbed is :

dQ = mL

where the same expansion is, change in volume = 0 so,

⇒ dW = PΔV = 0

so, dQ = dU + dW ⇒ dU = mL

Internal energy increases during the melting process

LIMITATION OF FIRST LAW OF THERMODYNAMICS

• The first law of thermodynamics will not show the direction of changes.
• This law fails to explain the heat flow. If the rod is heated, the heat flows from one hot end to the cold end.
• The amount of energy transfer is only described in the first law of thermodynamics.

SIGN CONVENTION IN THERMODYNAMICS SYSTEM

∆Q (+ve)

∆W (+ve)

∆Q (-ve) ∆W (-ve)

Work done	Heat	Sign
Work done By the system	Heat gained by the system	∆Q= +ve ∆W= +ve
Work done by the system	Heat lost by the system	∆Q= -ve ∆W= +ve
WorK done on the system	Heat gained by the system	∆Q=+ve ∆W=-ve
Work done on the system	Heat lost by the system	∆Q=-ve ∆W=-ve