# First Law of Thermodynamics

- This law is also called the
**law of conservation of energy**. - It can be
**stated in many ways**but the following form is found to be quite useful. - It states that “energy can neither be created nor destroyed. However, it can be transformed from one form into another”.
- This means that if
**certain amount of energy**of one kind disappears (used up), an exact equivalent amount of some other kind of energy is produced. - In other words, the first law of thermodynamics can be stated that the
**total energy of the universe**(system + surrounding) is**constant.**

Image source: geeksforgeeks

**Mathematical Formulation **

Let us consider a system in initial state having internal energy * E1*. If heat equal to

*is supplied to the system, and work equal to*

**q***is done on the system, then the internal energy of the system in the final state (*

**w***is given by,*

**E2)**E2 = E1 + q + w

E2 – E1 = q + w

∴ **ΔE ****= q + w**………………………. (1)

This relationship between internal energy, work and heat is the mathematical statement of the first law of thermodynamics.

Now, (i) If **w = 0** i.e., no work is done on the system, then

**ΔE ****= q **

i.e., the internal energy changes an equal amount to the amount of heat absorbed by the system.

(ii) If **ΔE = 0** i.e., there is no increase in the internal energy of the system, then

q = -w

i.e., work done by the system (on the surroundings) is equal to the heat absorbed by the system

(iii) We know that, **w = -P ΔV**

Substituting the value of * w* in equation 1, one gets

**ΔE ****= q – P ΔV** ………………………………….. (2)

**q – ΔE = P ΔV** …………………………………… (3)

Now, if the process is carried out under constant volume condition (i.e., **ΔV = 0**),

Then,

**ΔE = q _{v}**

i.e., the change in the internal energy of as system is equal to the heat absorbed by the system under constant volume conditions.

**Information provided by 1 ^{st} law of Thermodynamics**

From the first law, we learnt that

- Total energy of the universe i.e., the energy of the system and surroundings taken together remains constant.
- Different forms of energy are
**inter-convertible**i.e., one form of energy can be converted into another. - Whenever one form of energy disappears, an
**equivalent amount of**energy in another form appears.

**Limitations of the 1 ^{st} law of thermodynamics**

- This law
**does not tell us**anything about the**extent and direction**of the convertibility of one form of energy into another. **For example**, when two bodies which are capable of exchanging heat energy are brought in contact, from the first law we know that the heat gained by one must be equal to that lost by the other.- The first law of thermodynamics however, does not tell us which of the two would lose or gain heat energy.
- It also
**does not tell how much energy**would be transferred from one to the other. - But we know that the heat must flow from a body at higher temperature to that at the lower.

**References: **

i) https://opentextbc.ca/openstaxcollegephysics/chapter/the-first-law-of-thermodynamics/

ii) https://energyeducation.ca/encyclopedia/First_law_of_thermodynamics

iii) https://www.geeksforgeeks.org/first-law-of-thermodynamics/