Give the mathematical formation of first law of thermodynamics.

First law of thermodynamics : Law of conservation of energy is treated as first law of thermodynamics which state that energy is always conserved. Thus, energy can neither
be created nor be destroyed, but one form of energy can be converted into another form.
Mathematical form of first law of thermodynamics : Let a system in state ‘A’ of internal energy E_A absorb certain amount of heat (Q) from the surroundings and undergo a change in its state to ‘B’. Let the internal energy in the state ‘B’ is E_B. If ‘W’ is the workdone by the system in the process, the increase in  internal energy ($∆$E) of the system is given by the equation $∆$E = E_B -E_A . Net gain of energy is (Q–W). Form first law of thermodynamics, net gain of energy (Q–W)
must be equal to $∆$E . Hence,
$∆$E = (E_B -E_A ) - (Q - W) or Q = $∆$E + W
This is the mathematical form of first law of thermodynamics.