State the first law of thermodynamics. Explain its mathematical notation.

Explanation

First law of thermodynamics :
The law of conservation of energy is taken as the first law of thermodynamics.
Statements
i) "Energy can neither be created nor destroyed, although it can be transformed from one form to another
ii) it is impossible to construct a perpetual motion machine of first kind (which produce work without consuming energy)".
iii) The total energy of the system and surroundings is constant".
Mathematical form:
Let a system in state "A", of internal energy `E_A` absorb from the surroundings acertain amount of heat (Q) and undergo a change in its state to B. Let the internal energy in the state B is `E_B`. If .W is the work done by the system in the process, the increase in internal energy `triangleE` of the system is given by the equation. `triangleE=triangleE_B-triangleE_A`
System -A. `E_A to" System "-B, E_B`
From first law, net gain of energy (Q-W) must be equal to `triangleE`
`triangleE =(E_B-E_A)= (Q-W)`
(or) `Q=triangleE+ W`
For infinitesimally small changes `q=triangleE +W`
q= increase in internal energy + energy used in doing work.
Above equation is mathematical form of I law of thermodynamics