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# 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

2b1dQ- ∫2c1dQ –( ∫2b1dW – ∫2c1dW)
=0

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

2b1dQ =  2c1dQ

That is heat is
also a path function.