First law of thermodynamics

 It is nothing but the law of conservation of energy.

Closed system:

For a closed system, the law can be represented as

where Q is the heat input to the system considered
          W is the work obtained from the system
          dU is the change in internal energy of the working fluid of the system.

Let us consider a simple compression process in a piston cylinder arrangement.

 Before compression process, let the internal energy of the working fluid (say air) be U1.Due to compression internal energy of the working fluid increases considering the process as adiabatic (no heat exchange).Let it be U2.In this case, increase in the internal energy can be experienced as increase in pressure of the working fluid.
Then by first law

dU (U2-U1) = -W since Q=0 for an adiabatic process.

 -sign indicates that work is given to the system.

 

Cycle:

For a cycle, the law can be represented as

where ΣQ is the sum of the heat exchanges during various processes of a cycle
          ΣW is the sum of work input and output during various processes of the cycle.