This law is based on law of conservation of energy.
If δQ = Heat supplied to a thermodynamical system
δW= Work done by thermodynamical system
dU = Change in internal energy δQ = δW + du
(i) δQ, δW, and du must be in the same units.
Heat supplied to the system=(+)ve
Heat rejected by the system =(-)ve
Work done by the system=(+)ve
Work done on the system=(-)ve
If temperature increased dU=(+)ve
If temperature decreases dU=(-)ve
Heat is the energy which is transferred between a system and its environment because of the temperature difference between them. It is given by
δQ = mS?T
Where S is molar specific heat
Work is defined as the energy that is transferred from one body to the other owing the force that acts between them.
It is given by δW = PdV
Internal energy of a system if the energy possessed by the system due to molecular motion and molecular configuration. It is given by.
Now if we substitute all the above the value in the first law of thermodynamics. It becomes.