# First law of Thermodynamics :

First law of Thermodynamics is based on Energy conservation.

According to this law , work and heat both are the forms of energy and for a cyclic process , net heat transfer is equal to net work transfer.

i.e.,

### Qnet = Wnet

The result of first law is based on experiments and following points were also proposed :

(a) Energy can neither be created nor be destroyed.

(b) Internal Energy is energy in storage.

(c)When one form of energy exhaust , it mean it gets transformed to another form of energy.

on adding the above observation following result comes –

## ∆Q = dE + ∆W

Here ,

∆Q = Heat transfer

∆W = Work transfer

E = internal energy + kinetic energy+ potential energy

If , kinetic energy and potential energy are negligible

Then ,

E = Internal Energy ( U )

i.e., dE = dU

Therefore ,

## ∆Q = dU + ∆W

This is First law of Thermodynamics.

## Internal Energy :

It is the energy in storage of system at molecular level and includes molecular collisions, molecular kinetic energy, chemical energy, nuclear energy and many more microscopic energies.

Internal energy is :

• Property of system
• Point function
• Exact differential
• Cyclic integral is zero

For ideal gas , Internal Energy is the function of temperature only.

## Consequences of first law of Thermodynamics:

#### (a) Heat Transfer is a path function

To prove this , consider a P-V diagram as shown above .

For cycle , 1-A-2-B-1

∆Q1-A-2 + ∆Q2-B-1 = ∆ W1-A-2 + ∆W2-B-1

As ,∆Q1-A-2 = ∆ W1-A-2

Therefore , ∆Q2-B-1 = ∆W2-B-1___________eq(1)

For cycle 1- A-2-C-1

∆Q1-A-2 + ∆ Q2-C-1 = ∆W 1-A-2 + ∆W2-C-1

∆Q1-A-2 = ∆W 1-A-2

Therefore , ∆ Q2-C-1 = ∆W2-C-1 _________eq(2)

eq(1) – eq (2)

∆Q2-B-1 – ∆ Q2-C-1= ∆W2-B-1 – ∆W2-C-1 ____eq(3)

Here RHS is not equal to zero

Therefore , LHS will also not be equal to zero.

Conclusion ,

Here the final and initial point of both 2-B-1 and 2-C-1 are same but the heat transfer is unequal .Hence , it is not a point function as it doesn’t depend on initial and final condition.

Therefore heat transfer is a path function.

#### (b) Internal Energy is a point function :

From equation (3)

∆Q2-B-1 – ∆ Q2-C-1= ∆W2-B-1 – ∆W2-C-1

∆Q2-B-1 – ∆W2-B-1 = ∆ Q2-C-1 – ∆W2-C-1

From first law of thermodynamics

∆Q= dU + ∆W

OR

∆Q-∆W= dU

Therefore

dU2-B-1 = dU2-C-1

Process 2-B-1 and 2-C-1 are different while change in internal energy is same, it means internal energy is a point function.

#### (c) Energy of isolated system remains constant

For isolated system ,

∆Q = 0

∆W = 0

Therefore , dU will also be zero

i.e ., U = constant

#### (d) PMM-1 is not possible

Perpetual motion machine of first type is a hypothetical machine which can produce the work continuously without taking any energy from the outside.

It is impossible because it violates the first law of Thermodynamics.