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.