Thermodynamic law

First law of thermodynamics-

a. The heat and mechanical work are mutually convertible. According to this law when a close system is undergoes a thermodynamic cycle. The net heat transfer is equal to the work transfer. In other words, the cycle integral of work transfers.

Mathematically,

Cycle integral of  δQ = cycle integral of δW

b. The energy can neither be created nor destroyed throught it can be transformed from one form to another .

Heat transfer and work transfer take place . The net energy transfered to stored within the system and is known as stored energy or total energy of the system.

Cycle integral of  δQ−δW= dE

Now integrating 

Q1-2 - W1-2= E2- E1

For unit mass

q1-2- w1-2= e2-e1

E1= total energy of the system at state 1

= PE1+ KE1+U1=mgz1+(mv1/2)2 +U1

E2=PE2+KE2+U2=mgz2+(mv2/2)2+u2