Write and explain the first law of thermodynamics.

Explanation

The internal energy of a system can change through two modes of energy transfer: heat and work.
Let `DeltaQ` = Heat supplied to the system by the surroundings.
`DeltaW` = Work done by the system on the surroundings. `DeltaU` = Change in the internal energy of the system.
From principle of conservation of energy, `DeltaQ=DeltaU+DeltaW` ....(1)
is known as the first law of thermodynamics.
From equation (1) it is said that the energy (`DeltaQ`) supplied to the system goes in partly to increase the internal energy of the system (`DeltaU`) and the rest in work on the surrounding (`DeltaW`).
Alternative form of this equation is,
`DeltaQ-DeltaW=DeltaU`...(2)
The system may go from an initial state to final state in a number of ways.
For example, to change the state of a gas from (`P_1, V_1`) to (`P_2, V_2`), first change the volume of the gas from `V_1` to `V_2` keeping the pressure constant, then change the pressure from `P_1` to `P_2` by keeping the volume constant.
By second way, keeping volume constant and change the pressure of the gas from `P_1` to `P_2` to take the gas to `(P_2 ,V_2)`.
By third way, by changing both volume and pressure to take the gas to `(P_2,V_2)`.
When system is taken from one state to other `DeltaQ` and `DeltaW` are different for different path mean `DeltaQ` and `DeltaW` depend on the path but the difference `(DeltaQ - DeltaW)` is same for every path. Means `(DeltaQ - DeltaW)` is same for every path when the system taken from one state to other. So `(DeltaQ - DeltaW)` is path independent but it depend on the initial and final state of system.
`therefore` First law of thermodynamics `DeltaQ-DeltaW=DeltaU`
The first law of thermodynamics is obeyed in all the changes occurring in nature.
All these three terms must have same units when this law is applied.