First Law for Closed System Undergoing Change of State - thermodynamics:

In accordance to first law, when system undergoes a thermodynamic process (change of state) heat and work transfer of both take place. The net energy transfer is stored within the system and is called as stored energy or total energy of system.

When process is executed by system the change in stored energy of system is numerically equal to the net heat interaction minus net work interaction at the time of process.

  dE = dQ - dW                                                                                                   ...(i)

  E₂  - E₁  = Q₁-2  - W₁-2

Here E is an extensive property and represents total energy of system at a given state, that is,

E = Total energy

dE = dPE + dKE + dU

If there is no change in Potential Energy and Kinetic Energy
 then, PE = KE = 0 dE = dU, putting in equation (1), we get dU = dQ - dW

or                          dQ = dU + dW

This is the 1^st law of thermodynamics for the closed system. Here,

  dU = Change in Internal Energy dW = Work Transfer = PdV

  dQ = Heat Transfer = mcdT

{Heat added to system is taken as positive (+ve) and heat removal by the system is taken as negative} For a cycle              

 dU = 0; dQ = dW