# First law of thermodynamics

### The first law of thermodynamics is the thermodynamic
expression of **the conservation of energy**.

This law most simply stated by saying that “energy can not be
created or destroyed” or that “the
energy of the universe is constant”.

This law can be stated for a system (control mass) undergoing a
cycle or for a change of state of a system.

Stated for a system undergoing a cycle, the cyclic integral of the
work is proportional to the cyclic integral of the heat.

Mathematically stated, for a control mass undergoing a
cyclic process such as in Joule’s experiment and for consistent set of units

∫dQfrom system= ∫dWon system

or ∫dQfrom system- ∫dWon system = 0

The important thing to remember is that the first law states that
the energy is conserved always.

## **Sign convention **

The work done
by a system on the surroundings is treated as a positive quantity.

Similarly, energy transfer as heat to the system from
the surroundings is assigned a positive sign. With the sign convention one can write,

∫dQ = ∫dW

**Consequences of the
first law**

Suppose a system is taken from state
1 to state 2 by the path 1-a-2 and
is restored to the
initial state by the path 2-b-1, then the system has undergone a cyclic
process 1-a-2-b-1. If the system is restored to the initial state by path
2-c-1, then the system has undergone the cyclic change 1-a-2-c-1. Let us apply
the first law of thermodynamics to the cyclic processes 1-a-2- b-1 and
1-a-2-c-1 to obtain

∫1-a-2dQ+ ∫2-b-1dQ - ∫1-a-2dW - ∫2-b-1dW =0

Subtracting,
we get

∫1-a-2dQ+ ∫2-c-1dQ - ∫1-a-2dW - ∫2-c-1dW=0

∫_{2b1}dQ- ∫_{2c1}dQ –( ∫_{2b1}dW - ∫_{2c1}dW)
=0

We know that the work is a path function and hence the term in
the bracket is non-zero.
Hence we find

∫_{2b1}dQ = ∫_{2c1}dQ

That is heat is
also a path function.

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